The extremal Sombor index of trees and unicyclic graphs with given matching number

Abstract

In 2021, the Sombor index was introduced by Gutman, which is a new vertex-degree-based topological index. The Sombor index of a graph G is defined as , where d G (υ) is the degree of the vertex υ in G. Let and be the set of trees and unicyclic graphs on n vertices with fixed matching number m, respectively. In this paper, the trees and the unicyclic graphs with the maximum Sombor index among and are characterized, respectively.