The Sombor index of trees and unicyclic graphs with given matching number
Ting Zhou, Zhen Lin, Lianying Miao

TL;DR
This paper determines the trees and unicyclic graphs with the maximum Sombor index among those with fixed vertex count and matching number, expanding understanding of this topological index in graph theory.
Contribution
It identifies the extremal graphs with maximum Sombor index within classes of trees and unicyclic graphs constrained by matching number.
Findings
Identifies the tree with maximum Sombor index in _{n,m}
Identifies the unicyclic graph with maximum Sombor index in _{n,m}
Provides structural characterizations of extremal graphs
Abstract
In 2021, the Sombor index was introduced by Gutman, which is a new degree-based topological molecular descriptors. The Sombor index of a graph is defined as , where is the degree of the vertex in . Let and be the set of trees and unicyclic graphs on vertices with fixed matching number , respectively. In this paper, the tree and the unicyclic graph with the maximum Sombor index are determined among and , respectively.
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Taxonomy
TopicsGraph theory and applications · Computational Drug Discovery Methods · Synthesis and Properties of Aromatic Compounds
