Cacti with maximal general sum-connectivity index. (English) Zbl 1475.05112
Summary: 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.
MSC:
| 05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
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