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 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.

Maximum values of sombor index of bicyclic graphs with a given matching number

“…In this section, we show all the lemmas which will play important role to determine the maximum values for Sombor index. Denoted by U 2m,m the set consist of all unicyclic graphs with maximum matching number m of order n. Zhou et al [12] determined the following result (see Fig. 1).…”

Ordering Unicyclic Graphs with a Fixed Girth by Sombor Indices

“…Zhou et al [15] used a different approach, characterizing extremal trees and unicyclic graphs with the maximum and minimum Sombor index values, while considering the matching number as a relevant parameter. Similarly, in another study, Zhou et al [14] explored extremal Sombor index within the same graph class, taking into account a given maximum degree. Das et al [4] contributed to the field by establishing bounds on the Sombor index of trees considering order, number of pendant vertices and the independence number.…”

On the Extremal General Sombor Index of Trees with Given Pendent Vertices

“…Inspired by the work in [36], we investigate the General Sombor index for the trees having a given number of pendent vertices. Let N G (x) (or N (x)), represent the collection of neighboring vertices for a given vertex x ∈ V (G).…”