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 \(\alpha \geq 1\).