Applied Mathematics and Scientific Computing

In multiple attribute group decision-making (MAGDM) problems, weights of decision-makers play a vital role. In this paper, we present a new approach for finding the weights for decision-making process based on singular perturbation problem in which decision-makers’ weights are completely unknown. The attribute weights are derived using the exact and numerical solution for reaction-diffusion type problem. For the decision-making process, we utilize a class of ordered weighted averaging (OWA) operator, and the newly calculated decision-maker weights are used in the computations of identifying the best alternative from the available alternatives. The feasibility of the proposed method is displayed through a numerical illustration, and comparison is made with existing ranking methods.

Decision-making is a most powerful, well-organized, civic, and pecuniary effect. Power to produce logical and correct choices is the burden of any decision process imbued with uncertainty. In offices where the information or the data is of the form of intuitionistic trapezoidal fuzzy numbers, to construct the MAGDM problem, intuitionistic trapezoidal fuzzy weighted geometric (ITFWG) and intuitionistic trapezoidal fuzzy hybrid geometric (ITFHG) operators are applied. In this paper, a novel method of deriving the unknown decision-maker weights using Sumudu transform combined with integrodifferential equation is proposed, and the derived weights are used in computations for identifying the best alternative. A goodness of fit for this method is provided to show the effectiveness of the proposed approach.

We present meromorphic solution of the Riccati-Abel differential equation by considering the corresponding complex differential equation. Riccati-Abel differential equation is one of the most widely used equations of mathematical physics. A result from Nevanlinna theory that helps us in obtaining such a solution concerns sharing one value of meromorphic function and its first derivative.

This article considers uncertain parameters of a function as closed intervals. Expansion of these types of function in a single dimension is studied. μ-monotonic property of this function in higher dimension is introduced, and higher-order expansion in R n is developed using μ-monotonic property.

This article deals with the fractional Bloch equation by using Caputo-Fabrizio fractional derivative and Atangana-Baleanu fractional derivative with non-singular kernels. Bloch equation is extensively used in chemistry, physics, magnetic resonance imaging (MRI) and nuclear magnetic resonance (NMR). The nuclear magnetization M = (M x, M y, M z) is derived analytically, and its behaviour is discussed via plots for different fractional orders. A comparative study of the analytical solutions with Caputo-Fabrizio, Atangana-Baleanu and Caputo fractional derivatives is presented. Equilibrium stage is achieved faster via Atangana-Baleanu fractional derivative than other fractional derivatives.

Centre manifold theory, a useful tool in the study of dynamical systems, plays a crucial role in analysing the stability of the system. In the paper the three-dimensional manifold arising in the study of Rayleigh-Bénard-Brinkman convection in enclosures is reduced to a unidimensional manifold using a transformation dictated by the centre manifold theorem. Such a reduction is possible since the Lorenz model is autonomous. The advantage in this procedure is that the intractable Lorenz model gets reduced to a tractable Ginzburg-Landau equation and hence facilitates an analytical study of heat transport.

In this article we have introduced a class R ~ ( η , q , ς ) , η ∈ ℂ − { 0 } $$\mathcal {\tilde {R}}_{\varSigma }(\eta ,q,\varsigma ),\eta \in \mathbb {C}-\{0\} $$ of bi-univalent functions defined by symmetric q-derivative operator. We have estimated the upper bounds for the initial coefficients and Fekete- Szeg ö $$\ddot {o}$$ inequality by making use of Chebyshev polynomials.

In this paper, an adaptive mesh has been generated using the concept of entropy function for solving convection-diffusion singularly perturbed parabolic partial differential equations with a small delay. Similar problems are associated with a furnace used to process a metal sheet in control theory. The beauty of the method is, unlike the popular adaptive meshes (Bakhvalov and Shishkin), prior information of the width and position of the layers are not required. The method is independent of perturbation parameter ε and gives us an oscillation-free solution, without any user-introduced parameters. The applicability of the proposed method is illustrated by means of two examples.

Two-dimensional, steady, finite-amplitude Rayleigh-Bénard-Taylor convection of a Newtonian nanoliquid-saturated porous medium is studied using rigid-rigid isothermal boundary condition. The nanoliquid is assumed to conform to a single-phase description and occupies a loosely packed porous medium. Critical Rayleigh number and Nusselt number as functions of various parameters are analyzed, and this is depicted graphically. A non-zero Taylor number demands a higher temperature difference between the horizontal boundaries compared to that of a zero Taylor number case in order to initiate instability in the system and thus inhibits advection of heat. The isothermal boundaries of the rigid-rigid type do not allow as much heat to pass through as that by the free-free type, and hence we see a reduced heat transfer situation in the former case.

The numerical analysis of 3D magnetohydrodynamic Darcy-Forchheimer nanofluid flow with nonlinear thermal radiation is explored. Utilizing suitable similarity transformations, the governing PDEs are transformed into nonlinear ODEs. The resulting equations are then solved numerically by the most robust shooting technique with RK method of fourth order. The effect of various parameters like radiation, temperature ratio, Forchheimer and porosity parameters on θ(η) and ϕ(η), skin friction coefficient, and rate of heat transfer is discussed graphically. It is observed that the heat transfer rate reduces and skin friction coefficient increases for the rise of F r and λ.

The intention of this communication is to explore the significance of electromagnetohydrodynamic (EMHD) on the fluid transport properties of a chemically reacting nanofluid with two types of geometries. Simulations have been done to investigate the controlling equations by utilizing Crank-Nicolson scheme. Influence of embedded parameters such as Hartman number, heat source/sink, Brownian diffusion, chemical reaction, and thermophoretic diffusivity is graphically presented. Tables demonstrate the significant impact of sundry parameters on skin friction factor and heat and mass transfer rates. It is observed that the electrical field parameter has high influences on the fluid flow and heat transfer characteristics.

The key goal of the article is to examine the non-linear thermal radiation and double stratification effects on 3D MHD convective stream of nanoliquid over a non-linear stretchable surface in a porous medium. Using suitable transformations, the governing systems are converted into ODEs and are solved by using homotopy analysis method (HAM). While increasing thermal and solutal stratification parameter, the temperature decreases. The temperature enhances by raising the values of non-linear thermal radiation. The skin friction coefficient along x- and y-axis, local Nusselt number and Sherwood number are plotted for important parameter involved in the study, and the results are discussed in detail.

The intention of this communication is to explore the characteristics of electromagnetohydrodynamics on the fluid transport properties of a chemically reacting Casson fluid with two types of geometries. Formulations consist of salient features of radiative heat transfer, Lorentz force, and chemical reaction. This model is constituted with governing equations which are solved numerically by an efficient finite difference scheme of Crank-Nicolson type. Impact of pertinent parameters like Casson fluid, electrical field, Hartmann number, and chemical reaction is observed through graphs. The outcomes of surface shear stress, rate of heat, and mass transfers are presented through tables. Results enable us to state that larger electrical field decelerates the Casson fluid flow. Influence of the magnetic field on mean surface shear stress is more significant in the flow on a plate than that of cone.

In this study, analytical solutions are obtained for the unsteady flow of a viscous, incompressible fluid between two coaxial rotating disks of infinite dimensions, using the homotopy analysis method (HAM). Using similar variables, we first simplify the exact Navier–Stokes equation to highly coupled nonlinear partial differential equations. Upon application of the HAM these equations are replaced by a system of linear and uncoupled ordinary differential equations and solutions effective throughout the entire temporal and spatial domains are obtained. The nature of the flow fields is discussed under the influence of the same or opposite direction of rotation, Reynolds number, etc. Physically interesting quantities, such as radial and tangential shear stresses, are also obtained, and are valid throughout the temporal domain. To the best of our knowledge, no such series solution is available in the literature for the problem under consideration.

The thermal diffusion and diffusion-thermo effects on radiative mixed convective flow and heat transfer of Casson-Williamson fluid over a stretching surface are examined in the presence of uniform external magnetic field. The thermal radiation and chemical reaction effects are included in the study. This physical model is mathematically modelled by a set of nonlinear partial differential equations with boundary conditions. The governing system of equations is reformed into ordinary differential equations with the help of similarity variables, and then they are solved using homotopy analysis method. The concentration profile increases on increasing the dufour parameter, and the temperature profile increases on increasing the radiation parameter.

In the present paper, we study Brinkman-Bénard convection in nanoliquid-saturated porous enclosure with vertical walls being adiabatic and horizontal walls being isothermal for two velocity boundary combinations, namely, free-free (FF) and rigid-rigid (RR). Brinkman model has been modified in the present study to account for added nanoparticles. Thermophysical properties of nanoliquid in a saturated porous medium as a function of corresponding properties of base liquid, nanoparticle and porous medium are modelled using phenomenological laws and mixture theory. An analytical study has been made of Brinkman-Bénard convection in a porous enclosure using single-phase model. The effect of nanoparticles is to advance onset of convection and enhance heat transfer, whereas porous medium facilitates delayed onset and retainment of heat energy in the system. The present study shows good agreement with those of previous works.

The objective of the present paper is to examine numerically the chemical reaction and mass transfer effects on magnetohydrodynamic Williamson fluid past an exponentially stretching sheet. The basic flow field equations are transformed to coupled, nonlinear ordinary differential equations using suitable similarity variables and then solved using the Runge–Kutta–Fehlberg method. The effects of various material parameters on the flow field momentum and species in addition to wall shear stress are computed effectively and portrayed graphically. The diffusion rate is low for both homogeneous and heterogeneous reactions. Acceleration in the values of Williamson fluid parameters accelerates the friction.

Wall properties effect has been investigated on the peristaltic flow of Casson fluid in a channel by assuming long wavelength and low Reynolds number. The governing equations are solved analytically to find the expression for velocity and stream function. The effect of different parameters of wall and fluid properties on the velocity and stream function is discussed through graphs. The results obtained create interest among young researchers to concentrate on the wall effects of different types of Newtonian and non-Newtonian fluids in the presence of peristalsis.

The flow of a Jeffrey fluid is extended to include a Newtonian fluid through a vertical symmetric channel with peristalsis under the assumptions of long wavelength and small Reynolds number. The model is applicable to study the behavior in physiological systems. The velocity field, stream function, interface shape, pressure rise (drop), and frictional force at the wall over a cycle of wavelength are obtained, and the results are shown graphically. It is observed that the variation of interface shape yields the thinner peripheral region in the dilated region with increasing Jeffrey parameter λ 1 and thicker peripheral region in the dilated region for low viscosity ratio.

The Soret and Dufour effects on the peristaltic transport of a conducting Casson nanofluid in a flexible channel are studied. The influence of dissipation and Joule heating are also discussed. The governing equations are simplified by using a long wave length and small Reynolds number approximations. The analytical solutions for stream function and axial velocity are obtained. Moreover, the Runge–Kutte-based shooting method is utilized to solve the coupled energy and concentration equations. The impact of important parameters on the flow is explained using graphs for both Newtonian and Casson fluid cases. It is observed that the Casson fluid has more velocity than the Newtonian fluid in the middle of the channel and the situation is reversed at the channel walls. Further, a higher temperature is noted for Casson fluid than for Newtonian fluid throughout the channel, whereas concentration shows the opposite behavior.

This paper is concerned with the axisymmetric elastic waves in a transversely isotropic submerged piezoelectric rod coated with thin film using a constitutive form of linear theory of elasticity and piezoelectric equations. The equations of motion along radial and axial directions are decoupled by using potential functions. The surface area of the rod is coated by a perfectly conducting material, and no slip boundary condition is employed along the solid-fluid interactions. The dispersion equation which contains the longitudinal and flexural modes is derived and is studied numerically. To observe the variations of mechanical and electric displacement in the coated piezoelectric rod, the authors compute the numerical values of the field variables for the ceramic PZT − 4. The effects of fluid and coating environment on the variation of field variables are analyzed and presented graphically. This type of study is important in the modeling of underwater sensors for the navigation applications.

This paper aims at the study of numerical investigation into the three-dimensional steady-state flow of a nanofluid under the effect of thermal radiation as well as heat generation/absorption over a nonlinearly stretching sheet. The set of partial differential equations is transformed into ordinary differential equations by employing the suitable similarity transformations. The solution to the governing equation is obtained by using numerical techniques specifically the bvp4c function in MATLAB. A nonuniform velocity with power-law index is the boundary condition specified for solving the governing equation.

This study addresses the effects of unsteady MHD radiative slip flow of Williamson fluid due to the chemically reacting sheet with variable conductivity and heat source or sink. The boundary layer equations of the Williamson fluid model for heat and mass transfer are deliberated. The governing partial differential equations are transformed into a set of coupled ordinary differential equations of motion for Williamson fluid are modeled under the sheet and then solved numerically by the shooting technique with BVP4C package. The physical features of the model are presented and discussed in graphs and tables.

HIV/AIDS is a very challenging epidemic disease all over the world. In the present chapter, the homotopy analysis method (HAM) is functional for evaluating the estimated solution of the HIV dynamic model during primary infection. By using the HAM, we have adjusted and controlled the area of convergence of the infinite series solution with the help of auxiliary parameters. Numerical results for different cases obtained graphically show that series solutions are convergent and the residual errors curve shows that the HAM is very effective at gaining an accurate approximation.

The analysis on the changes due to mass and heat transfer in the presence of chemical reaction, thermal radiation, internal heat generation, and Dufour-Soret effects on an unsteady hydromagnetic combined convection stagnation-point flow toward a vertical plate embedded in a solutally and thermally stratified porous surrounding subjected to the slip conditions on velocity, thermal, and solutal fields is presented deliberately in this paper. Relations of similarity are inducted for the conversion of flow relations as ordinary differential equations and the solution is obtained upon the application of shooting method combined with Runge-Kutta algorithm. An analysis is presented upon the graphical depictions on the profiles of velocity of the liquid, its temperature, and its concentration with respect to some physical entities, and conclusions thereby are drawn.

Natural convection of nanoliquids confined in a low-porosity enclosure when the lateral walls are subject to constant heat and mass fluxes is studied analytically using modified Buongiorno-Darcy model and Oseen-linearised approximation. For the study we considered water-copper nanoliquid and aluminium foam, glass balls as porous materials. The effective thermophysical properties are calculated using phenomenological laws and mixture theory. An analytical solution is obtained for boundary layer velocity and Nusselt number. The study shows that dilute concentration of high thermal conductivity nanoparticles significantly facilitates enhanced heat transport. The porous medium, however, diminishes heat transport when the thermal conductivity of the porous material, k pm, is less compared to that of nanoparticles, k np. When k pm ≥ k np then the presence of nanoparticles does not affect the heat transport.

The flow of viscous, incompressible and electrically conducting fluid past and impermeable cylinder present in a cylindrical porous region is considered for the steady case in presence of magnetic field applied in vertical direction. The flow is governed by modified Brinkman and Stokes equations in porous and nonporous regions, respectively. The matching boundary conditions are used at the interface with no-slip condition at the solid surface and uniform velocity away from the nonporous region. This boundary layered problem is solved analytically and obtained solutions in terms of modified Bessel’s functions.

The present work addresses the two-dimensional boundary layer flow of a Powell-Eyring fluid over a stretching cylinder with binary chemical reaction and Arrhenius Activation energy. Also, considered Cattaneo-Christov heat flux model in the place of conventional Fourier’s law of heat conduction. Suitable transforms lead to strongly nonlinear differential equations, which are solved through R-K method along with shooting scheme. The effects of various parameters are shown graphically on velocity, temperature and concentration fields. The numerical values for skin friction( Re x X C f / 2 $$ \sqrt {{{{\mathop{\rm Re}\nolimits} }_x}} X{C_f}/2\ $$ ), local Nusselt(NuxRex-1/2 X-1) and Sherwood numbers(shxRex-1/2 X-1 are reported. A relative revision among the earlier published results and the present results for a special case is found to be in an excellent agreement. Rising the values of thermal relaxation time, reduces the temperature at near the cylinder due to domination of mixed convection in the flow.

The study investigates the effect of homogeneous-heterogeneous reactions in the stagnation point nanofluid flow toward a cylinder. In the presence of uniform magnetic field, thermal radiation, and non uniform heat source or sink. As per the geometry of the flow configuration, the conservation laws are transformed into a nonlinear model. Using the appropriate analogue transformations, the resultant equations are employing RK-4th order approach along with shooting technique to derive closed-form solutions for momentum, angular velocity, temperature, and concentration fields as well as skin friction, local Nusselt number, and Sherwood number. It is observed that heat generation parameter leads to enhance the temperature distribution. The concentration boundary layer thickness decreases for larger homogeneous reaction rate parameter.

The present article has been arranged to study the Hall current and Joule heating effects with thermal radiation on peristaltic flow of nanofluid in a channel with flexible walls. Convective conditions for heat transfer in the formulation are adopted. Viscous dissipation in energy expression is taken into account. Resulting differential systems after invoking small Reynolds number and long wavelength considerations are numerically solved. Runge-Kutta scheme of order four is implemented for the results of axial velocity, temperature, and concentration. Outcomes of new parameters like Brownian motion parameter, thermophoresis parameter, thermal radiation parameter, Prandtl number, and Eckert number on the physical quantities of interest are discussed. It is found that the influence of thermal radiation parameter and the Biot number on the temperature is the same fashion.

This article presents a numerical investigation on free convective heat and mass flow characteristics in a 3-dimensional MHD nonlinear boundary layer flow of nanofliuids past a deformed revolving surface through porous medium in the presence of Joule heating and radiation absorption as part of the chemical reaction mechanism. It is assumed that the Ag- water and Cu- water nanofluids which flow in parallel layers in a stream line. The phenomenon presided when modelled the flow transport leads to obtain a coupled nonlinear partial differential equations and further in the process of attaining an approximate solution, the system of equations were transformed in to a set of nonlinear ordinary differential equations using appropriate similarity transformation. The resulting equations were solved numerically with by using the R-K-Felhberg-integration with shooting method. It is found that the temperature increases with increasing radiation absorption parameter, We also seen that the Ag-water nanofluid has high thermal conductivity than Cu-water nanofluid.

In this article, we presented simultaneous solutions for magnetohydrodynamic Cattaneo-Christov flow of Carreau fluid over a variable thickness melting surface. Firstly, proper transformations are considered to convert the basic flow equations as ODE. The solution of these ODEs is obtained by the consecutive application of shooting and R.K. fourth-order methods. Graphs are plotted with the assistance of MATLAB package to emphasize the impact of various physical parameters on the flow fields. Further, the rate of heat transfer and friction factor are also intended and depicted with the help of a table. Results indicate that fluid velocity has inverse relationship with melting and magnetic field parameters. Also the nonuniform heat source/sink parameters play a key role in heat transfer performance.

Utilizing the linearized wave theory, the issue of the diffraction of obliquely progressive waves by a little contortion on a porous sea-bed is investigated. By the help of perturbation hypothesis, the related problem is diminished to a boundary value problem (BVP) for the first-order velocity potential function. Then the first-order potential function and, henceforth, the first-order reflection as well as transmission coefficients are evaluated by Fourier transform technique. A particular frame of sinusoidal ripples has been considered for verifying the theoretical results.

We examine a quasilinear system of PDEs governing the one-dimensional unsteady flow of a radiating van der Waals fluid in radial, cylindrical and spherical geometry. The local value of the fundamental derivative (Γ) associated with the medium is of order O(??) and changes sign about the reference state (Γ = 0); the undisturbed medium is assumed to be spatially variable. An asymptotic method is employed to obtain a transport equation for the system of Navier Stokes equations; the impact of radiation and the van der Waals parameters on the evolution of the initial pulse is studied.

The influence of slip and convective boundary heating on unsteady forced convective heat transfer of an electrically conducting incompressible fluid over a flat plate in the presence of uniform magnetic field along with chemical reaction is examined. The governing partial differential equations are transformed into ordinary differential equations by applying similarity transformations. Then the reduced equations are solved numerically by shooting technique and Runge-Kutta method and are solved analytically by homotopy analysis method.

In this paper, the homotopy perturbation method (HPM) has been used to solve some wave equations and a few heat equations. The resultant solution helps to substantiate that HPM is a useful and robust mechanism to solve these equations. An accurate approximation is possible while solving complex and complicated problems using semi-analytical methods, an example of which is the HPM. However, we consider the boundary conditions as one-dimensional when we use this method, and hence these approximations can be considered only for a small range. HPM was developed by J. H. He for solving wave and heat equations. To obtain accurate results for these equations using HPM, standard homotopy technique is merged with the perturbation technique along with some modifications.

Analysis of nonlinear radiative heat transfer on the MHD Maxwell fluid flow in the boundary layers adjacent to a sheet with continuous stretching is discussed. Numerical solution of the PDEs governing the flow is obtained by the successive application of suitable similarity variables and BVP4c method. The flow variables, surface frictional coefficient, and local gradients of temperature and concentration are discussed through the graphs and tables. Results of the present analysis are compared with the previously published work and are found to be in close agreement.

This study addresses the thermal energy transport in a slippery sheet-driven flow of a micropolar fluid analysing the effect of radiative heat flux. The solution of PDEs of the governing the flow is derived numerically by the application of self-similarity transformations and Runge-Kutta Fehlberg algorithm along with shooting method. The computational results are discussed graphically for several selected flow parameters. Results of this analysis are compared with the published results and are seen to tally very closely.

In this paper, analytical solutions for dimensionless fin temperature distribution and dimensionless fin heat transfer rate are derived and offered for a two-dimensional orthotropic, pin fin structure with contact resistance at the fin base in a convective environment. Fin performance was evaluated based on the different forms of ratio of conductive resistance to convective resistance parameters Bi r, Bi z, Bi c, thermal conductivity ratio K ∗, and dimensionless length of fin contact space at the base δ ∗. The detailed discussions on dimensionless parameters lead to the deterministic design and optimization of polymer composite fin structures under all types of convective situations in many real-time applications.

This work numerically explored the developing laminar natural convection in the vertical double-passage cylindrical annuli. The double-passage annuli are designed from three upright coaxial cylindrical tubes with the intermediate cylinder treated as a thin and conductive baffle. In the present study, two thermal conditions are imposed, namely, interior or exterior cylindrical wall is constantly heated, whereas the opposite wall is thoroughly insulated. Using the boundary layer approximation, the nonlinear and coupled governing partial differential equations are numerically solved by employing an implicit finite difference technique. The flow and thermal distributions, heat transfer rates are portrayed for various axial locations, Grashof number and baffle position. The results reveal that the velocity and temperature profiles significantly altered with Grashof number and axial locations. Further, the baffle location plays a major role in controlling the heat transfer in the annular passages.

We discussed Hall effects on unsteady hydromagnetic natural convective rotating flow of second grade fluid past an impulsively moving vertical plate entrenched in a fluid inundated porous medium, while temperature of the plate has a temporarily ramped profile. Analytical solutions of the governing equations are obtained by Laplace transform technique. The precise solution is also obtained in case of unit Schmidt number. The analytical phrases for skin friction due to primary and secondary flows and Nusselt number are derived for both ramped temperature and isothermal plates. Expression for Sherwood number is also obtained. The velocity, temperature, and concentration are displayed graphically, whereas those of skin friction, Nusselt number, and Sherwood number are presented in tabular form with reference to momentous flow parameters.

High-power light emitting diode (HPLED) is an emerging technology in automotive, aerospace, domestic, and industrial lighting applications. Application of HPLED in the above mentioned areas are challenging, as effective cooling is required for maximal luminous output and longer life. This chapter deals with estimation of the total luminous flux of HPLED using a mathematical model for a given heat sink configuration, and electric and thermal conditions. The parameters that are considered in this model are voltage, current, the power of HPLED, the number of the LEDs in the module, thermal parameters such as the junction temperature of LED, heat sink and fin temperature, ambient temperature, and thermal resistances. The proposed model will be helpful for designing and predicting the luminous output of LED and also arriving at optimal heat sink and fin configurations for a given design.

The present study explores the effects of thermal radiation, chemical reaction, viscous dissipation, Soret and Dufour on Marangoni convection over a steady and laminar boundary layer flow. A nanofluid, consisting of copper, silver, and alumina metallic nanoparticles suspended in water, is considered. Similarity transformations are used to solve the governing equations of motion. The transformed ordinary differential equations are then solved numerically using MATLAB ‘bvp4c’ residual method. The upshots of various physical properties influenced by Eckert, Nusselt, Sherwood, Soret, and Dufour numbers are delineated.

Let G = (V, E) be a simple, finite, connected, and undirected graph. Let D ⊆ V (G) be the non-empty subset of V (G) such that D is the minimum distance-2 dominating set in the graph G = (V, E). If V − D contains a distance-2 dominating set D ′ of G, then D ′ is called an inverse distance-2 dominating set with respect to D. The inverse distance-2 domination number γ ≤ 2 − 1 G $${{\gamma }_{\leq 2}}^{-1}\left (G\right )$$ of G is the minimum cardinality of the minimal inverse distance-2 dominating set of G. In this paper, we presented an algorithm for finding an inverse distance-2 dominating set of a graph.

A uniquely colorable graph G whose chromatic partition contains at least one γ-set is termed as a γ-uniquely colorable graph. We characterize the planarity of these graphs using the domination number of G.

In this paper, a technique of coding a message is presented using the super mean labeling on a two star graph K 1,m ∪ K 1,n, m ≤ n. A method of fixing the super mean labeling on any two star graph is provided after stating a few observations for a super mean labeling on a two star graph in order to use the combination of the two for coding.

This article is devoted to present the first status connectivity indices and its coindices of some composite graphs such as join, Cartesian product, corona product, and composition of two given connected graphs.

The concept of Laplacian energy of an intuitionistic fuzzy graph is extended to Laplacian energy in operations on intuitionistic fuzzy graph. In this paper, we have obtained the value of Laplacian energy in different operations such as union and join between two intuitionistic fuzzy graphs. Also we study the relation between the Laplacian energy in the operations on two intuitionistic fuzzy graphs.

Binary trees are enormously used in data structure as they can be easily stored, manipulated, and retrieved. The most straightforward and extensive applications of binary trees are in the study of computer searching and sorting methods, binary identification problems, and variable binary codes. Many complex networks are easily classified and analyzed by the usage of binary tree representations. A binary tree is defined as a tree in which there is exactly one vertex of degree two and each of the remaining vertices is of degree one or three. Every binary tree is a rooted tree with odd number of vertices. A special type of binary tree known as hypertree is an interconnection topology which combines the easy expansibility of tree structures with the compactness of the hypercube. In this paper we find the Wiener index of hypertree.

Locating-2-Dominating Set is denoted as R 2 D ( G ) $$R_{2}^{D}(G)$$ , and in this chapter the Location-2-domination number for direct and Cartesian product of graphs, namely P n □ P m $${{P}_{n}}\square {{P}_{m}}$$ , P n □ S m $${{P}_{n}}\square {{S}_{m}}$$ , P n □ W m $${{P}_{n}}\square {{W}_{m}}$$ , C n □ C m $${{C}_{n}}\square {{C}_{m}}$$ , P n × P m, P n × S m, C n × P m, C n × C m, are being found.

Let G = (V, E) be a connected graph and W ⊆ V be a nonempty set. For each u ∈ V , the set f W(u) = {d(u, v) : v ∈ W} is called the distance pattern of u with respect to the set W. If f W(x) ≠ f W(y) for all xy ∈ E(G), then W is called a local distance pattern distinguishing set (or a LDPD-set in short) of G. The minimum cardinality of a LDPD-set in G, if it exists, is the LDPD-number of G and is denoted by ϱ ′(G). If G admits a LDPD-set, then G is called a LDPD-graph. In this paper we discuss the LDPD-number ϱ ′(G) of some family of graphs and the relation between ϱ ′(G) and other graph theoretic parameters. We characterized several family of graphs which admits LDPD-sets.

Minimizing the total power in a wireless sensor network (WSN) has great significance, since the nodes are powered by a small battery of limited capacity. By using an appropriate topology, the energy utilization of the network can be minimized which results in an increased lifetime of a WSN. In reality, WSN is modeled as an undirected graph in which each vertex represents a sensor node and an edge represents the link between the two sensor nodes. We define a distance function that maps a pair of vertices to a positive real number, i.e., Euclidean distance between the two vertices. On this initial topology, we construct a reduced topology satisfying special connectivity constraints like bi-connectivity, k-connectivity, bounded diameter, degree restricted, etc. We assign power to each node as the maximum distance of all its adjacent edges, and total power of the network is the sum of the powers of all the vertices. Fault tolerance addresses the issue of a node or link failure in a WSN. Fault-tolerant network aims at k-connectivity in the network so that there exist at least k vertex disjoint paths between any two sensor nodes of the network. Minimum power 2-connected subgraph (MP2CS) problem is to contrive a 2-connected network with minimum total power. It is proved that MP2CS problem is NP-hard. Minimum power k backbone node 2-connected subgraph (MPkB2CS) problem is a special case of MP2CS problem, which seeks a power assignment satisfying 2-connectivity with k backbone nodes. In this paper, the problem of finding a 3-connected network for a given set of nodes, which minimizes the total power with k backbone nodes, is addressed which is termed as MPkB3CS problem. We propose an algorithm for MPkB3CS problem and establish that the proposed algorithm has an approximation ratio of 4k + 1, for k ≥ 3.

A fuzzy inference system works on the basis of fuzzy if-then rules to mimic human intelligence for quantifying the vagueness/uncertainty, which arises in many real-world problems. In this paper, fuzzy inference system is designed using triangular and hendecagonal fuzzy number that represent the value for the linguistic environment. The factors of T2DM mellitus play a critical role in affecting each and every individual health without their knowledge. In this paper, the factor of “Blood Glucose”, medical term known as hyperglycemia, is analyzed through this fuzzy inference system (FIS).

In this article, we compute the Narayana prime cordial labeling of book graphs using prime and Narayana numbers.

A simple graph G(V, E) has order p and size q. Let f : V ( G ) → ℤ 4 − { 0 } $$f : V(G) \to {\mathbb Z}_4 - \{0\}$$ be a function. For each E(G) define f ∗ : E ( G ) → ℤ 3 $$f^* : E(G) \to {\mathbb Z}_3$$ by f ∗ ( u v ) = f ( u ) f ( v ) ( mod 3 ) $$f^*(uv) = \left \lceil \frac {f(u)}{f(v)} \right \rceil (\text{mod } 3)$$ where f(u) ≥ f(v). The function f is said to be quotient-3 cordial labeling if the difference between the number of vertices (edges) labeled with i(k) and the number of vertices (edges) labeled with j(l) by atmost 1. 1 ≤ i, j ≤ 3, i ≠ j, and 0 ≤ k, l ≤ 2, k ≠ l. Here it is proved that some path-related graphs like (P n;P 2), S(P n;P 2), [P n;S m] m ≠ 1, S[P n;S 2], Twig(Tg n), and S(Tg n) are quotient-3 cordial.

In this paper, a new parameter on domination is defined by imposing a restriction on the degrees of vertices in the dominating set. For a positive integer k, a dominating set D of a graph G is said to be a k-part degree restricted dominating set (k-DRD-set), if for all u ∈ D there exists a set C u ⊆ N(u) ∩ (V − D) such that | C u | ≤ ⌈ d ( u ) k ⌉ $$|C_u| \leq \lceil \frac {d(u)}{k}\rceil $$ and ⋃u ∈ D C u = V − D. The minimum cardinality of a k-part degree restricted dominating set of G is called the k-part degree restricted domination number of G and is denoted by γ d k ( G ) $$\gamma _{\frac {d}{k}}(G)$$ . Here, we determine the k-part degree restricted domination number of some well-known graphs, relation between dominating and k-DRD set, and an algorithm which verifies whether a given dominating set is a k-DRD set or not.

b-Coloring of G is a coloring which is proper such that in each color class there exists a vertex which is called as representative vertex that has at least one neighbor in each of the remaining color classes. The highest positive integer k such that the k-colors can be used to color the vertices of G along with b-coloring is the b-chromatic number of G, denoted by b(G). For a given graph G with n vertices, G ∗ is constructed (Jeeva et al., Indian J Math 59(2):255–261, 2017). In the research paper, we find out the b-chromatic number of Mycielskian, splitting, shadow, middle, and total graph of G ∗.

Achieving a reliable and secure communication is the major challenge in the context of data communication and storage. In this paper, Encode-then-Encrypt framework is defined using linear error correcting codes and elliptic curves to address these challenges as a single solution rather than addressing them separately. The working of the proposed framework is explained in detail by taking Reed-Solomon codes (with a set of encoding and decoding algorithms) and elliptic curves of characteristic 2 (with a set of encryption and decryption algorithms). We have outlined the advantages of using such elliptic curves and error correcting codes over any other cryptosystem defined in the existing literature. The proposed framework can be implemented as a part of any real-time communication system to ensure reliability and security.

An induced acyclic graphoidal decomposition (IAGD) of a graph G is a collection ψ of nontrivial induced paths in G such that every edge of G lies in exactly one path of ψ and no two paths in ψ have a common internal vertex. The minimum cardinality of an IAGD of G is called the induced acyclic graphoidal decomposition number denoted by η ia(G). In this paper we present bounds for η ia(G) in terms of cut vertices and simplicial vertices of G.

The Laplacian energy of an intuitionistic fuzzy graph concept is extended to dominating Laplacian energy in various products of intuitionistic fuzzy graph. In this paper, we have obtained the value of dominating Laplacian energy in two products such as Cartesian product and tensor product. Also we study the relation between the dominating Laplacian energy in the products in two intuitionistic fuzzy graphs.

A set S of vertices in a graph G is called a dominating set of G if every vertex in V (G)∖S is adjacent to some vertex in S. A set S is said to be a power dominating set of G if every vertex in the system is monitored by the set S following a set of rules for power system monitoring. The power domination number of G is the minimum cardinality of a power dominating set of G. In this paper, we obtain the power domination number for triangular graphs, pyrene networks, circum-pyrene networks, circum-trizene networks, generalized honeycomb torus and honeycomb rectangular torus.

Implementation of parallel algorithms and simulation of different interconnection networks need an effective tool, that is, graph embedding. This paper focuses on improving a lower bound obtained in Rajan et al. (Comput J 58:3271–3278, 2015) for dilation of an embedding onto circulant networks. In addition, this paper provides algorithms to compute dilation of embedding circulant network into certain trees, for instance, m-rooted complete binary tree, m-rooted sibling tree, and r-dimensional hypertree, proving that the improved bound obtained is sharp.