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Open problem on the maximum exponential augmented Zagreb index of unicyclic graphs

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Abstract

A topological index is a numerical property of a molecular graph that explains structural features of molecules. The potential of topological indices to discriminate between distinct structures is a significant topic to investigate. In this context, the exponential degree-based indices were put forward in the literature. The present work focuses on the exponential augmented Zagreb index (EAZ), which is defined for a graph G as

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

where \(d_i\) represents the degree of the vertex \(v_i\)and E(G) denotes the edge set of G. This work characterizes the maximal unicyclic graph for EAZ in terms of graph order, which was posed as an open problem in the recent article Cruz et al. (MATCH Commun Math Comput Chem 88:481-503, 2022).

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Acknowledgements

The authors are grateful to the referees for their valuable comments, which have considerably improved the presentation of this paper. K. C. Das is supported by National Research Foundation funded by the Korean government (Grant No. 2021R1F1A1050646).

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Authors and Affiliations

  1. Department of Mathematics, Sungkyunkwan University, Suwon, 16419, Republic of Korea

    Kinkar Chandra Das, Sourav Mondal & Da-yeon Huh

  2. Department of Mathematics, College of Sciences, University of Sharjah, Sharjah, 27272, UAE

    Sourav Mondal

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  1. Kinkar Chandra Das
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  2. Sourav Mondal
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Correspondence to Sourav Mondal.

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Das, K.C., Mondal, S. & Huh, Dy. Open problem on the maximum exponential augmented Zagreb index of unicyclic graphs. Comp. Appl. Math. 43, 317 (2024). https://doi.org/10.1007/s40314-024-02815-2

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  • DOI: https://doi.org/10.1007/s40314-024-02815-2

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