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Journal of Applied Mathematics and Computing

Erschienen in:

26.01.2024 | Original Research

On the exponential augmented Zagreb index of graphs

verfasst von: Kinkar Chandra Das, Sourav Mondal, Da-yeon Huh

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1/2024

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Abstract

A topological index is a numerical descriptor in mathematical chemistry and graph theory that quantifies a molecule’s structural properties without considering its three-dimensional arrangement. A crucial factor to consider when exploring topological indices is their capacity to distinguish between different structures. In light of this, the exponential vertex-degree-based topological index is put forward in the literature. The present work focuses on investigating the mathematical properties and application potential of the exponential augmented Zagreb index (EAZ). The EAZ index for a graph $\Upsilon $ is defined as

$$\begin{aligned} EAZ(\Upsilon )=\sum \limits _{v_iv_j \in E(\Upsilon )}\,e^{\displaystyle {\left( \frac{{d_i\,d_j}}{d_i+d_j-2}\right) ^{3}}}, \end{aligned}$$

where $d_i$ represents the degree of a vertex $v_i$. Crucial upper and lower bounds of EAZ for numerous classes of graphs like bipartite, unicyclic, bicyclic, chemical graph, and general graphs are derived. The bounds are computed in terms of different graph parameters including graph order, size, maximum degree, number of pendant vertices and independence number. The extremal graphs for which the bounds appear are also characterized. Moreover, the EAZ index is found to correlate well with some physico-chemical properties of octanes.

Vorheriger Artikel An exponential split-step double balanced Milstein scheme for SODEs with locally Lipschitz continuous coefficients

Nächster Artikel On distance Laplacian spectral ordering of some graphs

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Titel: On the exponential augmented Zagreb index of graphs
verfasst von: Kinkar Chandra Das
Sourav Mondal
Da-yeon Huh
Publikationsdatum: 26.01.2024
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 1/2024
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-023-01982-5

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