Skip to main content
Top

2024 | Book

Applied and Computational Mathematics

ICoMPAC 2023, Sukolilo, Indonesia, September 30

insite
SEARCH

About this book

This book collects selected, peer-reviewed research presented at the 8th International Conference on Mathematics: Pure, Applied, and Computation, held in Lombok, Indonesia, on 30 September 2023. Organised into three parts—Part I: Control Systems, Mathematical Simulation and Modeling; Part II: Formal Methods and Data Science; Part III: Graph Theory and Analysis—the book contains 29 peer-reviewed chapters. Ranging from theoretical to applied results, the book addresses the mathematical models for several phenomena such as investment behavior, unmanned surface vehicles and electronic medical records. It also highlights the progress in the use of satisfiability methods and tools to solve puzzle and pencil games. It showcases how mathematics is used to solve real-world problems.

Table of Contents

Frontmatter

Applied Mathematics (Control Systems, Mathematical Simulation, and Modeling)

Frontmatter
Simulation of Investment Behaviors Using Risk-Influenced Utility Models of Health and Wealth
Abstract
Recently, people have been paying much attention to health and financial investments, aiming for a better quality of life and financial security. This study introduces utility functions that operate as two-variable adaptations of several widely recognized one-variable utility functions, typically used by risk-averse investors. We demonstrate through analytical methods that these utility functions depict the substitutionary preference between two investment options. We aim to apply a bi-variate utility function within the utility maximization framework that incorporates two risks. There is a lack of longitudinal data on the returns of health investments. Most studies categorize people’s level of health broadly and only report the yearly percentages of the population in each category without detailing the effects of individual health investments. In the present paper, we show a model that defines the return on an individual health investment for this kind of health-level data. We also develop a methodology to simulate people’s investment choices based on their preference for maximum utility. The results help us understand better the costs involved, the extent of investment coverage, and the relationship between two investment choices. Ultimately, it offers a detailed view of the observed population’s investment behavior, providing valuable insights for future studies and strategies.
Helena Margaretha, Nicholas Satyahadi, Ferry Vincenttius Ferdinand
Wave Attenuation by a Combination of Mangroves and Reefball
Abstract
Porous breakwaters serve an important role in protecting the coastline by damping the incoming wave. Before implementing these breakwaters, a thorough study is required to assess their effectiveness. We present a mathematical model to examine wave attenuation caused by a combination of reefball and mangroves, serving as both submerged and emergent porous breakwaters, using modified shallow water equations. Our model includes a two-layer representation to account for both types of breakwaters. We then determine the wave transmission coefficient, which represents the degree of wave damping achieved by the combined breakwaters, using a numerical simulation. In addition, we analyzed the relationship between the dimensions of the breakwaters and the wave transmission coefficient. From this study, the result implies that the modified mathematical model has successfully captured the phenomenon and that wave amplitude reduction can be achieved by employing a greater value in the breakwater’s friction coefficient and domain.
Rianda Kumala Dewi, Indriana Marcella, Ikha Magdalena
Resonance Detection in a Semi-closed Basin with Constant Height and Triangular Width
Abstract
In this paper, our aim is to identify the presence of the resonance phenomenon within a semi-closed basin by introducing a rectangular, smooth-surfaced submerged breakwater. The basin in question possesses a constant height and a triangular width. To address this problem, we employ the modified Shallow Water Equations as our mathematical model. To determine the natural period of the basin, we utilize the Separation of Variables Method to solve the modified Shallow Water Equations analytically. Subsequently, we employ the Finite Volume Method on a staggered grid to solve the model numerically. By incorporating the natural period obtained from the analytical solution into the simulation, we can observe the occurrence of the resonance phenomenon within the basin. Additionally, we investigate the influence of the basin’s characteristics on this phenomenon. The results of this study indicate that adding one block of smooth-surfaced submerged breakwater is not enough to stop resonance from occurring. We also notice that the height, thickness, and location of the breakwater could affect the natural period and wave elevation. This acquired knowledge is expected to provide crucial insights for the future development of more reliable and effective coastal protection methods.
R. M. Valerio, I. Magdalena
Comparison of Ridge Regression and Principal Component Regression in Overcoming Multicollinearity of Factors Affecting Poverty in Indonesia
Abstract
Regression analysis is a statistical method that aims to measure the correlation or relationship between the independent variables on the dependent variable. The Regression analysis has several assumptions that must be met to obtain a good model. One of the assumptions that must be fulfilled is the absence of multicollinearity between the independent variables. Multicollinearity is a situation where there is a relationship or correlation between independent variables which causes the accuracy of the model to decrease. This study aims to compare ridge regression and Principal Component Regression (PCR) in overcoming multicollinearity. Ridge regression is a modification of the least squares method that adds a bias constant to the main diagonal of the variance–covariance matrix. The calculation of the bias constant in this study uses the Kibria method. Principal component regression is a combination of Principal Component Analysis (PCA) and regression analysis, this method works by regressing the main components. The comparison criteria used are \({R}^{2}\) and \({R}_{adj}^{2}\). The research data used is on factors influencing poverty in Indonesia in 2021. Based on the calculation results, it is found that the accuracy of the ridge regression model is 83.6%, while the accuracy of the principal component regression model is 77.5%, this value is seen from the largest value of \({R}^{2}\). Furthermore, the \({R}_{adj}^{2}\) value of the ridge regression model is greater than the \({R}_{adj}^{2}\) value of the principal component regression model, namely 0.7991 > 0.761. Thus, it can be concluded that ridge regression with Kibria parameters is better than principal component regression in overcoming multicollinearity in data on factors that influence poverty in Indonesia.
R. Rahmawati, L. Harsyiah, Z. W. Baskara
On Identification on Class of Nonlinear Control System with Relative Degree Two
Abstract
In this paper, we identify a specific class of nonlinear control system relative to degree two. We identify specific class nonlinear systems by using coordinate transformation to determine the normal form. Here, we construct some theorems that state the nonlinear system has a non-minimum phase, minimum or weak minimum.
Ahmadin, Janson Naiborhu, Fatmawati, Windarto
Implementation of K-Means Particle Swarm Optimization for Clustering Football Players in the Top Five European Football Leagues
Abstract
Football Clubs are prioritize victory and championship aspirations, requiring skilled players proficient in goal-scoring, precise passing, error reduction, and tactical comprehension. The objective of this study is to identify and analyze the most effective clustering approach and performance outcomes of football players using the combined methodology of k-means clustering and particle swarm optimization. The research data employed in this study consists of spatio-temporal information pertaining to the performance of football players. The outcomes of the k-means clustering, in conjunction with PSO, employing values of k ranging from 2 to 4, reveal that cluster k \(=\) 3 represents the most desirable group of players for recruitment recommendations by football clubs, with a silhouette coefficient of 0.76. Furthermore, the clustering process yields Cluster 1, comprising players capable of playing in three positions, Cluster 2 consisting of players specialized in one position, and Cluster 3 encompassing players adept at playing in two positions.
Adam Fahmi Khariri, Putroue Keumala Intan, Moh. Hafiyusholeh, Ahmad Hanif Asyhar, Aris Fanani
A Short Review of Numerical Modelling for Photocatalytic Degradation in Dye Systems
Abstract
This paper reviews the recent development of numerical modelling of photocatalytic degradation in dye systems. The focus of this study is mathematical modelling and numerical approach. The numerical models for simulating photocatalytic degradation processes are classified into three main categories: computational fluid dynamics (CFD), finite difference method (FDM) and finite element method (FEM). CFD is the most popular way to analyze the behaviour of photocatalytic systems due to effective experimental results prediction under varying physical and chemical conditions. FDM effectively solves the time-dependent partial differential equation of the diffusion process in photocatalytic materials over time. FEM is highly accurate for optimizing and simulation the diffusion of Fick’s law for two- or three-dimensional photocatalytic models. Fundamentally, the methods and numerical approach are carefully chosen to obtain meaningful results of the photocatalytic degradation rate. This review is intended to reference theoretical and experimental studies of photocatalytic degradation systems especially, in dye cases.
Muhammad Yusuf Hakim Widianto, Chairul Imron, Basuki Widodo
Reference Tracking of Quadrotor Using Modified Nonlinear Model Predictive Control Based on Nonlinear Disturbance Observer
Abstract
This paper proposes a modified nonlinear model predictive control based on nonlinear disturbance observer (NDO-NMPC) for reference tracking of a quadrotor. The quadrotor model is nonlinear with a multi-input-multi-output (MIMO) system type. This study’s discussed problem is requiring a quadrotor to track the given trajectories. The disturbances considered in the system are constant and step disturbances. The unknown disturbances are estimated using a nonlinear disturbance observer. Furthermore, the disturbance estimations are added to the system’s prediction of NMPC. Based on the simulation results, the NDO can provide good estimation results for estimating the system disturbances. According to the performed numerical simulations, the optimal inputs obtained satisfy the limitations of the defined constraints. In addition, the proposed NDO-NMPC can overcome external disturbances, so the outputs of NDO-NMPC are appropriate for the expected results.
S. Subchan, Leila Rizky Amalia, Tahiyatul Asfihani, Heri Purnawan
System Analysis and Numerical Simulation on Sedimentation Rates Considering the Dredging Factor
Abstract
This article discusses the system analysis of the dynamics of sedimentation rate by considering environmental factors. The modeling begins with constructing a seagrass growth model as a bioindicator of sedimentation rate based on dredging. The model is analyzed by looking for balance and stability points. Understanding the sedimentation behavior is imperative in determining their stability with varying the sedimentation dredging, a numerical simulation was carried out. The dredging parameter of numerical results shows that there is a Hopf bifurcation at \({\text{H}}=0.044121\) and a Saddle-Node bifurcation at \({\text{H}}=0.089756.\) Dredging can stabilize the sedimentation rate and growth of seagrasses in the ecosystem over a long period of time.
Dian Savitri, M. Jakfar, Laras K. M. Putri
A Mixed Integer Nonlinear Programming for Allocation Polyethylene Terephthalate (PET) Waste Management in Reverse Logistics Network
Abstract
The involvement of many parties in the municipal waste management process is a challenge to increasing reverse logistics performance. In this research, an integrated model for a reverse logistics network on municipal waste management will be developed to minimize the total cost of reverse logistics activities. The developed model will be structured in Mixed Integer Nonlinear Programming (MINLP). The purpose of this paper is to discuss the mathematical model and PET waste management under government subsidy. The Reverse Logistics structure implemented in Polyethylene Terephthalate (PET) waste management involves four echelons; PET waste generation, scavengers, collectors, and remanufacturers. The numerical examples show that the minimum total cost of PET waste management in the Reverse Logistics Network is IDR 120,737,487.00. The model shown in this paper can assist the players in deciding on the allocation and recycling process the PET waste.
Hilyatun Nuha, Nurhadi Siswanto, Erwin Widodo
Quantum K-Nearest Neighbors for Object Recognition
Abstract
Object recognition research is essential to simulate human vision capabilities on computers or robots. As time goes by, this research is getting more sophisticated, but it encounters challenges in the form of 3V: (volume) large volume of data; (variety) large variety of data; (velocity); and the need for fast data processing. That matter has led scientists to start looking for solutions to these problems. On the other hand, the development of quantum computing has opened up new opportunities in Quantum Machine Learning (QML), which combines the power of quantum computing with machine learning techniques. One of the exciting algorithms in QML is Quantum k-Nearest Neighbors (QKNN), which can be used in image-based object recognition. However, the use of QKNN in image-based object recognition is still limited and needs to be developed further. This research aims to apply and analyze the quantum computing-based QKNN algorithm in image-based object recognition. The steps include representing the image as quantum states, calculating the distance between two quantum states using the fidelity method, and determining the label using a majority vote based on the closest distance. In this study, the test of QKNN algorithm used 84 synthetic image data sets with a ratio of 64:20. The experimental results on the 2-class variety, the QKNN succeeded on average 0.80, show that the QKNN algorithm can recognize objects with an accuracy rate of 0.65 on the 4-class data set. Based on these results, there is a need for further study in terms of data fidelity and data preprocessing techniques to improve QKNN’s performance.
Ahmad Zaki Al Muntazhar, Dwi Ratna Sulistyaningrum, Subiono
Adaptive Kalman Filter for Automated Actuator Fault Diagnosis in Unmanned Surface Vehicle
Abstract
Actuator systems in unmanned surface vehicles (USV) are prone to failure. To guarantee safe and successful autonomous operations, actuator systems must be monitored. However, sensors monitoring actuator systems are often unavailable. Hence, the actuator fault must be estimated. This paper presents an adaptive Kalman filter (AKF) algorithm for actuator fault estimation in USV based on position, velocity, and orientation sensors. Numerical results show the benefit of using the AKF. Furthermore, the presented method is validated using a USV with an actuator fault in the experiment.
Tahiyatul Asfihani, Fadia Nila Sihan Novita Lutfiani, Ahmad Maulana Syafi’i, Subchan Subchan, Agus Hasan
A Moving Average Genetic Algorithm (MA-GA) for Estimating the COVID-19 Dynamic Based on a Stochastic SIRD Model
Abstract
In this study, we examine the transmission of the COVID-19 outbreak using a constructed SIRD stochastic model. To determine the most appropriate model parameters, three stochastic models are proposed, and genetic algorithms (GA) are employed. However, the standard GA has proven inadequate in obtaining suitable parameters for the model, leading to occasional discrepancies in tracking trends from actual case data. To overcome this limitation, we propose a novel modification of the genetic algorithm, termed the Moving Average Genetic Algorithm (MA-GA). Unlike the standard GA, our MA-GA continuously updates the parameters at predetermined intervals, resulting in significantly improved accuracy. By applying this method, we achieve higher precision in providing solutions for the stochastic SIRD model, thereby enhancing its ability to accurately reflect the real-world dynamics of the COVID-19 outbreak.
Endah R. M. Putri, Aldi E. W. Widianto, Amirul Hakam, Venansius R. Tjahjono, Hadi Susanto
A General Solution of Black–Scholes Equations on Some Rainbow Options
Abstract
This study proposes a general solution of the Black–Scholes equation to determine some Rainbow options’ prices, both analytically and semi-analytically. We formulate general analytical solutions in non-dimensional terms by appropriately treating the payoff conditions. In particular, we present analytical solutions for three types of rainbow options: Better of options, Exchange options and Spread options. Furthermore, as our second contribution, we propose a semi-analytic solution for these three types of Rainbow options, leveraging the Homotopy Perturbation Method (HPM). The simulation results demonstrate the remarkable proximity of the semi-analytic solution to the analytical solution, ensuring accurate option pricing approximations.
Amirul Hakam, Endah R. M. Putri, Lutfi Mardianto
Dynamic Response of Floating Crane During Lifting Operation: A Parametric Study
Abstract
The necessity of decommissioning aging offshore structures requires heavy lifting activities using floating cranes. Hence, studies related to the dynamic response of floating cranes are essential to better understand this process and enhance safety and security. The study on offshore heavy lifting in this paper is conducted using the Boundary Element Method (BEM) and Finite Element Method (FEM). These methods serve as alternatives to laboratory testing for studying the dynamic response of floating cranes during offshore heavy lifting operations. Five (5) parameters are developed to assess their sensitivity to the dynamic response, namely suspended load, waves, crane swings, vessel draft, and mooring tension. The results demonstrate that all these parameters significantly influence the dynamic response of the floating crane. The dynamic load factor on the crane hook's static load is calculated to be 1.21, a value in accordance with the recommendations provided by classification societies. These findings indicate that the present methods are feasible for determining the Dynamic Factor under specific conditions.
Fahmy Ardhiansyah, Rudi Walujo Prastianto, Murdjito, Ketut Suastika, Setyo Nugroho

Computational Mathematics (Formal Methods and Data Science)

Frontmatter
Efficient SAT-Based Approach for Solving Juosan Puzzles
Abstract
Juosan is a single-player paper-and-pencil puzzle introduced in 2014 and shown to be NP-complete in 2018. This NP-completeness implies that the Juosan puzzle is polynomial-time reducible to the Boolean satisfiability (SAT) problem, thereby allowing us to transform the puzzle into SAT problems. This paper introduces an efficient SAT-based approach for solving the Juosan puzzles. We first discuss the rules and derived properties of Juosan puzzles and translate them into Boolean formulas in Conjunctive Normal Forms (CNF). We show that the number of clauses and propositional variables used in the encoding is polynomially proportional to the puzzle’s size. Using this encoding, we successfully implement a declarative program with no search algorithm using MiniSAT in C++ to solve any Juosan puzzle with up to \(1350\) cells in less than one second on a standard personal computer. Experimental results show that our SAT-based approach outperforms the optimized backtracking algorithm for larger puzzles.
Muhammad Tsaqif Ammar, Muhammad Arzaki, Gia Septiana Wulandari
Modeling Path Puzzles as SAT Problems and How to Solve Them
Abstract
This paper discusses a SAT-based approach for solving the Path Puzzles—one-player paper-and-pencil puzzles recently proven NP-complete in 2020. The properties and rules of Path Puzzles are encoded into propositional formulas in Conjunctive Normal Forms (CNF). We describe the step-by-step derivation for such formulas and analyze the number of clauses and variables used to express them. Experimental results show that our declarative SAT-based solver in PySAT outperforms the conventional imperative backtracking technique for solving larger puzzles.
Joshua Erlangga Sakti, Muhammad Arzaki, Gia Septiana Wulandari
A Trustworthiness Scoring Model for Reviews Using a Graph Structure
Abstract
It refers to determine whether a product is good or bad at first glance because reviews mixedly contain positive or negative opinions. In this study, we propose a method to estimate users’ and stores’ trustworthiness using the network structure. Our method is based on the idea of eigenvector centrality and the Hypertext Induced Topic Selection (HITS) algorithm. The average value of the user’s usefulness obtained from P Yelp dataset tended to be higher when the user’s trustworthiness was higher.
Tanabe Hiroto, Kimura Masaomi
Non-linear Reward Deep Q Networks for Smooth Action in a Car Game
Abstract
We formulate non-linear reward functions on deep Q networks in a car racing game by observing the environment (simulator). We aim to control the car movement (action) more smoothly in the game simulator than in the original. Existing studies about deep reinforcement learning maintained either discrete or non-linear reward functions without considering the environment domain, which may lead to illogical car movements. For instance, the car is blocked by three other cars, yet the game still continues by jumping to one of them. To overcome the issues, we define a non-linear reward function to compute the penalty game score based on the distance between the car and the one in front of it. From the game simulator, we surprisingly enjoy the results from the proposed reward function as the car drives more accurately and smoothly than the SOTA models, even at the start of the game point, by showing the smallest number of crashes and no zigzaggy agent movement when the obstacles are far from it.
Mohammad Iqbal, Achmad Afandy, Nurul Hidayat
College Student Activity Recognition from Smartwatch Dataset
Abstract
We present a framework to recognize college student activities by monitoring their movements from the smartwatch. The goal of this work is to support smart educational systems by giving daily college student activity info. The proposed framework comprises a way to collect the college student trajectories and apply machine learning models to recognize their activities. Moreover, the proposed framework collects additional information from the smartwatch, which can elevate the accuracy of recognition. In the experiments, we observed three college students for 2 months in Department of Mathematics, Institut Teknologi Sepuluh Nopember. As a result, we introduce a benchmark dataset for college student activity recognition, namely, CSARD. Further, we compiled several machine learning models on CSRAD. The experiment results showed the highest accuracy coming from the random forest model with all features.
Arthur de Clairval, Laurent Alain Erwin Schuler, Mathis Franck Rellier, Mohammad Isa Irawan, Imam Mukhlash, Mohammad Iqbal
LTL Model Checking for Verification of Electronic Medical Record (EMR) Design
Abstract
This paper presents an in-depth investigation into the verification of a software design model, focusing on the context of Electronic Medical Record (EMR) systems. Verification plays a critical role in ensuring the correctness and reliability of such systems, making it a topic of paramount importance. In this study, we undertake the task of remodeling the EMR requirements using a finite transition system to facilitate rigorous analysis and verification. Additionally, we express the formal specification through Linear Temporal Logic (LTL), leveraging its expressive power and ability to capture temporal properties accurately. To assess the validity of the design model, we employ the widely recognized SPIN model checker, a tool known for its effectiveness in detecting errors and inconsistencies in software systems. Our analysis reveals several critical findings. Specifically, the model checker successfully identifies paths within the design model that fail to satisfy the specified LTL formula, shedding light on potential areas of concern. Moreover, the generation of a comprehensive counterexample provides valuable insights for further analysis and improvement of the software design. Overall, this research highlights the significance of verification techniques in software design and emphasizes the applicability of the finite transition system and LTL in this context. The findings underscore the importance of thorough verification and the potential benefits of employing tools like SPIN to enhance the reliability and robustness of EMR systems.
Acep Taryana, Dieky Adzkiya, Muhammad Syifa’ul Mufid, Imam Mukhlash, Alessandro Abate
Multi-feature Subgraph Fusion with Text Knowledge on Citation Link Prediction
Abstract
We propose multi-feature subgraph fusion neural networks to predict the citation links. We aim to refine the sparsity of the subgraph feature of citation links among articles. The proposed model fuses four features: subgraph of social network metrics, metadata article info, Word2Vec, and tf-IDF of the articles. Basically, we focus on the edge list feature level instead of the graph level since we can avoid the heavy computation for the adjacency matrix. However, we may neglect the similarity between articles in the text domain. Henceforth, we fuse with text knowledge from the articles, such as the corpus embedding and metadata of the articles. The proposed model was evaluated on a public dataset for link prediction. We can enjoy the proposed model performances by showing the ablation study on the fusion feature(s).
Ghaluh Indah Permata Sari, Hsing-Kuo Pao, Rudy Cahyadi Hario Pribadi, Mohammad Iqbal
Predicting Poverty Percentage Based on Satellite Imagery and Point of Interest Using Support Vector Regression and Random Forest Regression (Case Study of Central Java Province)
Abstract
The percentage of poverty in Indonesia is quite high, on the island of Java there are provinces that have a percentage above 10%, one of which is the province of Central Java. This problem occurs because data collection is carried out conventionally with surveys and censuses so that it requires human resources, time, and large costs. Remote sensing that uses satellite imagery and Point of Interest (POI) data can provide lower costs and shorter time. The use of machine learning is often used in predicting poverty by using Support Vector Regression (SVR) with Random Forest Regression (RFR). Satellite image and POI were extracted using zonal statistics, consisting of NTL, NDVI, NDBI, NDWI, LST, CO, SO2, NO2, and POI density data. Estimating the poverty percentage in Central Java in 2021 using a method between SVR and RFR with a tenfold cross validation procedure. The regions in Central Java with low poverty percentages are Semarang City and Salatiga. There are 12 districts that have a low poverty percentage. The best model to estimate poverty in Central Java is the SVR model with the lowest MAPE, MAE, and RMSE values. The prediction results of poverty percentage in Central Java get 20 districts correctly predicted. The correlation value between actual and predicted is quite high and the average percentage error value is quite low so the model obtained is optimal.
I Komang Pande Prajadhita Wibawa Putra, Irhamah, Nur Iriawan, Kartika Fithriasari
Preliminary Analysis of Isabelle Proof Assistant in Graph Programming Verification with GP2
Abstract
GP2 is a graph transformation rule-based graph programming language that facilitates analysis and verification of programs. Verification of a graph program with GP2 can be done with formal proof in first-order or monadic second-order logic. The process of verifying a graph program tends to be complex if it is done manually. This paper discusses the result of the preliminary analysis of the utilization of Isabelle as a proof assistant to help show the validity of a graph program. This study aims to see how much Isabelle can be used as a proof assistant to verify a graph program in GP2. Experimental results show that complex theory is one of the factors in Isabelle’s failure to prove certain properties. The research results show that Isabelle can verify some properties for graph program verification, but it is limited to certain theories.
Martin Hutapea, Gia Septiana Wulandari, Muhammad Arzaki

Pure Mathematics (Graph Theory and Analysis)

Frontmatter
Nonlocal Edge Metric Dimension on Corona Multiproduct Graphs
Abstract
The nonlocal metric dimension of a graph \(G\), denoted \({{\text{dim}}}_{{\text{nl}}}\left(G\right)\) is known as the cardinality of the smallest nonlocal resolving set \(W\) in \(G\). \(W\) resolve any vertices \(u\) and \(v\) that are not adjacent in G based on the distance from \(u\) and \(v\) to each vertex in \(W\). In this study, a subset of vertices \({W}_{E}\) is called a nonlocal edge resolving set in \(G\) if \({W}_{E}\) resolve any two edges \({e}_{i}\) and \({e}_{j}\) in \(G\) where both are not adjacent. Thus, \({e}_{i}\) and \({e}_{j}\) have different representations to \({W}_{E}\). The cardinality of minimum \({W}_{E}\) is called the nonlocal edge metric dimension and is denoted by \({{\text{edim}}}_{{\text{nl}}}\left(G\right)\). The purpose of this study is to introduce the concept of nonlocal edge metric dimensions and further analyze graphs with certain neighboring characteristics. In this study, a multiproduct corona graph \(G{\odot }^{k}H\) was used. The graph \(G{\odot }^{k}H\) was obtained from \((G{\odot }^{k-1}H)\odot H\). The research was conducted by reviewing the literature and constructing several multiproduct corona graphs for analysis of nonlocal edge metric dimension value patterns. The output of this research is getting the form of new characteristics and theorems regarding metric dimensions of nonlocal edges, especially in multiproduct corona graphs.
Rinurwati, D. W. Setyawati, Soleha, I. Herisman, K. Baihaqi, Sadjidon, T. I. Haryadi
The Vertex Degree of Relative G-Noncommuting Graph of the Dihedral Groups
Abstract
Let G be a finite group, H be a subgroup of G, and g be a fixed element of G. The relative g-noncommuting graph \(\Gamma _{g, H, G}\) of G is defined as a graph with the vertex set G where two distinct vertices x and y are adjacent if \([x,y] \ne g\) and \([x,y] \ne g^{-1}\), and at least one of x or y belongs to H. This paper will discuss the vertex degree of the relative g-noncommuting graph for the dihedral group \(D_{2n}\), focusing specifically on cases where n is an even number. In this dihedral group, only two types of subgroups will be discussed, namely \(H=\langle a\rangle \) and \(H=\{e, a^j b \mid a,b \in G \}\) for some \(j=0,1, \dots , n-1\). Additionally, we will examine several topological indices of the relative g-noncommuting graph, including the first Zagreb index, the Wiener index, the edge Wiener index, the Hyper Wiener index, and the Harary index.
Nur’Ain Supu, Intan Muchtadi Alamsyah, Erma Suwastika
On Conformable Fractional Riesz Bounded Variation of Order
Abstract
In this paper, inspired by the concept of conformable fractional (CF) derivative of order \(\alpha\) with the definitions of Riesz bounded \(p -\) variation and Lipschitz continuous function, we introduce the new definitions of CF Riesz bounded variation and CF Lipschitz continuous function, respectively. Furthermore, we give some of its important properties and the relationships among those functions. In particular, the following chain of inclusions holds:
$$\rm{\mathbb{D}}^{\alpha} \left[ {a,b} \right] \subset \rm{{\mathbb{L}}{\mathbb{I}}{\mathbb{P}}}^{\alpha} \left[ {a,b} \right] \subset \rm{{\mathbb{B}}{\mathbb{V}}}^{\alpha,p} \left[ {a,b} \right] \subset \rm{{\mathbb{B}}{\mathbb{V}}}^{\alpha,q} \left[ {a,b} \right].$$
where \(\alpha \in \left( {0,} \right.\left. 1 \right]\) and \(p,q \in \left( {1,\infty } \right)\) where \(q < p\).
Supriyadi Wibowo, Christiana Rini Indrati
The Wiener Index, the Harmonic Index, and the Graph Representation of the Prime Ideal Graph for the Integers Modulo Rings with Prime Power Order
Abstract
The Wiener index and the Harmonic index of a graph are significant metrics in the realm of graph theory, offering valuable perspectives on the graph's structure, characteristics, and behavior. This research aims to determine the form of the representation of prime ideal graphs in the modulo integer ring with prime power order, and its topological indices such as the Wiener index and the Harmonic index. The graph is empty when the order is prime, and the graph contains complete subgraph and star subgraph when the order is prime power. Next, we can find the Weiner index and the Harmonic index of the graph. With the help of the complete subgraph and star subgraph mentioned earlier, we can find the Wiener index and the Harmonic index of the graph.
Hindani Kusuma Ningrum, Evi Yuniartika Asmarani, I Gede Adhitya Wisnu Wardhana, Salwa, Zata Yumni Awanis
Multiplicative Sum Nano Zagreb Index of Various 2-Power Corona Graphs
Abstract
For a simple and connected graph \(G\) with edge set \(E_{G} ,\) the multiplicative sum nano Zagreb index of \(G\) is \(\chi N*Z\left( G \right) = \mathop \prod \nolimits_{{uv \in E_{G} }} \left( {d^{2} \left( u \right) - d^{2} \left( v \right)} \right)^{\frac{1}{2}}\) with \({ }d\left( u \right){ }\) and \(d\left( v \right)\) are the degree of vertices \({\text{uu}}\) and \(v\) in \(G\) respectively. In this paper, this multiplicative sum nano Zagreb index of the \(G\) graph is introduced. Other than that some new graph operations are defined, those are 2-Power Corona and 2-Power Edge Corona graphs. The index for the 2-Power Corona and 2-Power Edge Corona graphs is determined and analyzed further.
Rinurwati, M. C. Fansury, A. H. G. K. Saefulloh, T. I. Haryadi
Metadata
Title
Applied and Computational Mathematics
Editors
Dieky Adzkiya
Kistosil Fahim
Copyright Year
2024
Publisher
Springer Nature Singapore
Electronic ISBN
978-981-9721-36-8
Print ISBN
978-981-9721-35-1
DOI
https://doi.org/10.1007/978-981-97-2136-8

Premium Partners