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arXiv · 2103.04645

The Sombor index of trees and unicyclic graphs with given matching number

Ting Zhou·Zhen Lin·Lianying Miao
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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 $G$ is defined as $SO(G) =\sum_{uv\in E(G)}\sqrt{d^2_G(u)+d^2_G(v)}$, where $d_G(v)$ is the degree of the vertex $v$ in $G$. Let $\mathscr{T}_{n,m}$ and $\mathscr{U}_{n,m}$ be the set of trees and unicyclic graphs on $n$ vertices with fixed matching number $m$, respectively. In this paper, the tree and the unicyclic graph with the maximum Sombor index are determined among $\mathscr{T}_{n,m}$ and $\mathscr{U}_{n,m}$, respectively.

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Ting Zhou, Zhen Lin, Lianying Miao. 2021-03-08. The Sombor index of trees and unicyclic graphs with given matching number. https://arxiv.org/abs/2103.04645

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