On the Maximum Atom-Bond Sum-Connectivity Index of Graphs

TL;DR

This paper investigates the maximum atom-bond sum-connectivity index among graphs with specific parameters, providing exact maximum values and characterizations for various graph classes.

Contribution

It determines the maximum ABS index for connected graphs with fixed parameters and characterizes the extremal graphs, advancing understanding of this topological index.

Findings

Maximum ABS index for graphs with fixed parameters identified

Extremal graphs characterized for each parameter class

Provides formulas and structural insights for maximizing ABS

Abstract

The atom-bond sum-connectivity (ABS) index of a graph $G$ with edges $e_1,\cdots,e_m$ is the sum of the numbers $\sqrt{1-2(d_{e_i}+2)^{-1}}$ over $1\le i \le m$, where $d_{e_i}$ is the number of edges adjacent with $e_i$. In this paper, we study the maximum values of the ABS index over graphs with given parameters. More specifically, we determine the maximum ABS index of connected graphs of a given order and with a fixed (i) minimum degree, (ii) maximum degree, (iii) chromatic number, (iv) independence number, or (v) number of pendent vertices. We also characterize the graphs attaining the maximum ABS values in all of these classes.