Extremal trees for Maximum Sombor index with given degree sequence

Let \(G=(V, E)\) be a simple graph with vertex set \(V\) and edge set \(E\). The Sombor index of the graph \(G\) is a degree-based topological index, defined as $$SO(G)=\sum_{uv \in E}\sqrt{d(u)^2+d(v)^2},$$ in which \(d(x)\) is the degree of the vertex \(x \in V\) for \(x=u, v\). In this paper, we...

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Bibliographic Details
Published in:arXiv.org 2022-11
Main Author: Movahedi, Fateme
Format: Article
Language:English
Subjects:
Graph theory
Trees (mathematics)
Vertex sets
Online Access:Get full text
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Summary:Let \(G=(V, E)\) be a simple graph with vertex set \(V\) and edge set \(E\). The Sombor index of the graph \(G\) is a degree-based topological index, defined as $$SO(G)=\sum_{uv \in E}\sqrt{d(u)^2+d(v)^2},$$ in which \(d(x)\) is the degree of the vertex \(x \in V\) for \(x=u, v\). In this paper, we characterize the extremal trees with a given degree sequence that maximizes the Sombor index.
ISSN:2331-8422