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Research Article | Open Access

On the maximum atom-bond sum-connectivity index of unicyclic graphs with given diameter

Zhen Wang1,2, Kai Zhou1,2( )
School of Big Data and Artificial Intelligence, Chizhou University, Chizhou 247000, China
Applied Mathematics Research Center, Chizhou University, Chizhou 247000, China
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Abstract

Let G=(V(G),E(G)) be a simple connected graph with vertex set V(G) and edge set E(G). The atom-bond sum-connectivity (ABS) index was proposed recently and is defined as ABS(G)=∑uv∈E(G)dG(u)+dG(v)−2dG(u)+dG(v), where dG(u) represents the degree of vertex u∈V(G). A connected graph G is called a unicyclic graph if |V(G)|=|E(G)|. In this paper, we determine the maximum ABS index of unicyclic graphs with given diameter. In addition, the corresponding extremal graphs are characterized.

Keywords

atom-bond sum-connectivity indexunicyclic graphdiameterpendent vertex
CLC number: 05C12, 05C35

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AIMS Mathematics
Volume 9 Issue 8,
August 2024
Pages 22239-22250
DOI: 10.3934/math.20241082

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Wang Z, Zhou K. On the maximum atom-bond sum-connectivity index of unicyclic graphs with given diameter. AIMS Mathematics, 2024, 9(8): 22239-22250. https://doi.org/10.3934/math.20241082

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Received: 25 May 2024
Revised: 02 July 2024
Accepted: 09 July 2024
Published: 15 August 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)