On Sombor index of graphs with a given number of cut-vertices

TL;DR

This paper investigates the minimum Sombor index among connected graphs with a fixed number of cut-vertices, characterizing the extremal graphs and contributing to graph theory and chemical modeling applications.

Contribution

It determines the minimum Sombor index for graphs with given vertices and cut-vertices, and characterizes the extremal graphs achieving this minimum.

Findings

Identified the minimum Sombor index in G^k_n

Characterized extremal graphs with minimum Sombor index

Extended understanding of Sombor index in graph classes

Abstract

Introduced by Gutman in 2021, the Sombor index is a novel graph-theoretic topological descriptor possessing potential applications in the modeling of thermodynamic properties of compounds. Let G^k_n be the set of all n-vertex connected graphs with k cut-vertices. In this paper, we present minimum Sombor indices of graphs in G^k_n. The corresponding extremal graphs have been characterized as well.