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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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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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