Maximum atom-bond connectivity index with given graph parameters

TL;DR

This paper investigates the maximum atom-bond connectivity (ABC) index in connected graphs with fixed parameters, characterizing extremal structures and providing conjectures and numerical analysis.

Contribution

It introduces new characterizations of extremal graphs for the maximum ABC index under various fixed graph parameters.

Findings

Characterized extremal graphs for maximum ABC index.

Provided conjectures on extremal structures.

Presented numerical analysis of extremal values.

Abstract

The atom-bond connectivity (ABC) index is a degree-based topological index. It was introduced due to its applications in modeling the properties of certain molecular structures and has been since extensively studied. In this note, we examine the influence on the extremal values of the ABC index by various graph parameters. More specifically, we consider the maximum ABC index of connected graphs of given order, with fixed independence number, number of pendent vertices, chromatic number and edge-connectivity respectively. We provide characterizations of extremal structures as well as some conjectures. Numerical analysis of the extremal values are also presented.