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Cacti with maximal general sum-connectivity index

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Abstract

Let V(G) and E(G) be, respectively, the vertex set and edge set of a graph G. The general sum-connectivity index of a graph G is denoted by \(\chi _\alpha (G)\) and is defined as \(\sum \limits _{uv\in E(G)}(d_u+d_v)^\alpha \), where uv is an edge that connect the vertices \(u,v\in V(G)\), \(d_u\) is the degree of a vertex u and \(\alpha \) is any non-zero real number. A cactus is a graph in which any two cycles have at most one common vertex. Let \(\mathscr {C}_{n,t}\) denote the class of all cacti with order n and t pendant vertices. In this paper, a maximum general sum-connectivity index (\(\chi _\alpha (G)\), \(\alpha >1\)) of a cacti graph with order n and t pendant vertices is considered. We determine the maximum general sum-connectivity index of n-vertex cacti graph. Based on our obtained results, we characterize the cactus with a perfect matching having the maximum general sum-connectivity index.

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Acknowledgements

The author would like to express his sincere gratitude to the referees and the editor for their careful reading of this article and for all their insightful comments, which leads a number of improvements to this paper. The author, is a PhD candidate (CSC, Student ID 2017280093) is highly thankful to the Chinese Government Scholarship Council for their unconditional financial support throughout his PhD studies.

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Authors and Affiliations

  1. Department of Mathematics, University of Sialkot, Sialkot, 51310, Pakistan

    Shahid Zaman

  2. Faculty of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, People’s Republic of China

    Shahid Zaman

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  1. Shahid Zaman
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Correspondence to Shahid Zaman.

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Zaman, S. Cacti with maximal general sum-connectivity index. J. Appl. Math. Comput. 65, 147–160 (2021). https://doi.org/10.1007/s12190-020-01385-w

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  • DOI: https://doi.org/10.1007/s12190-020-01385-w

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