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Title:
A Variant of Atom Bond Sum Connectivity Index
Authors:
Mohammed Yasin H, Suresh M, Sourav Mondal
Volume
94
Issue
3
Year
2025
Pages
761-782
Abstract

Topological index is a numerical graph invariant derived from molecular graph. The atom bond sum connectivity index drew a lot of interest from chemical graph theorists in a short period of time. Nowadays, the degree sum of a vertex's first neighbors is recognized as a useful parameter in chemical graph theory. Keeping these two facts in mind, the neighborhood degree sum based \(ABS\) index (\(NABS\)) is put forward in this study. It is defined as \begin{equation*} NABS(G) = \sum_{uv \in E(G)} \sqrt{\frac{\mu_{G}(u) + \mu_{G}(v) - 2}{\mu_{G}(u) + \mu_{G}(v)}}, \end{equation*} where \(\mu_{G}(u)\) represents the sum of degrees of all the vertices in a graph \(G\) adjacent to the vertex \(u\). The role of this index in structure-property modelling and isomer discrimination is investigated. The extremal graphs for \(NABS\) are identified in case of tree, bipartite, unicyclic and general graphs in terms of different graph parameters including graph order and size, maximum and minimum degree, independence number, chromatic number, etc.