journal-of-discrete-mathematical-sciences-and-cryptography Journal of Discrete Mathematical Sciences and Cryptography 2169-0065 0972-0529 Taru Publications 10.1080/09720529.2021.2015090 The extremal Sombor index of trees and unicyclic graphs with given matching number Zhou Ting School of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu, 221116, China Lin Zhen School of Mathematics and Statistics, Qinghai Normal University, Xining, Qinghai, 810001, China Miao Lianying School of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu, 221116, China 26 8 2205 2216 17 08 2022

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 dG(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.

 Tree Unicyclic graph Sombor index Matching number access open retracted no