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Title:
Maximum Atom-Bond Sum-Connectivity Index in Unicyclic Graphs of Fixed Girth
Authors:
Palaniyappan Nithya, Suresh Elumalai, Selvaraj Balachandran, Hechao Liu
Volume
94
Issue
3
Year
2025
Pages
783-804
Abstract

The \(ABS\) (atom-bond sum-connectivity) index of a graph \(G\) is given by the formula: \[ABS(G) = {\sum\limits_{xy\in E(G)}} \sqrt{\dfrac{{d_x}+{d_y}-2}{{d_x}+{d_y}}},\] where \({d_x}\) denotes the degree of vertex \(x\) in the graph \(G\). The primary objective of this research paper is to identify the maximum, and second-maximum \(ABS\) index among all unicyclic graphs with a fixed girth. Additionally, we provide a characterization of the specific graphs that attain these extreme \(ABS\) values.