Trees with a Given Order and Matching Number that Have Maximum General Sum-Connectivity Index

Abstract

The general sum-connectivity index is defined as ${\chi }_{\alpha }(G)=\sum _{uv\in E(G)}(d_G(u)+d_G(v){)}^{\alpha }$. Let $\mathcal{T}(n,\beta )$ be the class of trees of order $n$ with given matching number $\beta$. In this paper, we characterize the structure of the trees with a given order and matching number that have maximum general sum-connectivity index for $0<\alpha <1$ and give a sharp upper bound for $\alpha \ge 1$.