On Sombor Index of Unicyclic graphs with a fixed number of pendant vertices
Joyentanuj Das, Yogesh Prajapaty
TL;DR
This paper determines the maximum Sombor index for unicyclic graphs with a fixed number of pendant vertices and identifies the unique graph achieving this maximum.
Contribution
It introduces the first characterization of the maximum Sombor index in unicyclic graphs with a given number of pendant vertices.
Findings
Identified the maximum Sombor index for the class of unicyclic graphs.
Established the unique graph structure that attains this maximum.
Provided a mathematical proof for the extremal graph.
Abstract
The Sombor index is a topological index in graph theory defined by Gutman in 2021. In this article we find the maximum Sombor index of unicyclic graphs with a fixed number of pendant vertices. We also provide the unique graph among the chosen class where the maximum Sombor index is attained.
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Taxonomy
TopicsGraph theory and applications · Graph Labeling and Dimension Problems · Commutative Algebra and Its Applications