General cut method for computing Szeged-like topological indices with applications to molecular graphs

TL;DR

This paper introduces a universal cut method for calculating a broad class of Szeged-like topological indices in molecular graphs, unifying and extending previous approaches with applications to various chemical graph families.

Contribution

It formally defines a general Szeged-like topological index and provides a cut method for its computation on any weighted graph, broadening the scope of existing techniques.

Findings

Unified computation method for Szeged-like indices

Closed-form formulas for specific molecular graph families

Application to benzenoid, phenylene, and coronoid systems

Abstract

Szeged, PI and Mostar indices are some of the most investigated distance-based molecular descriptors. Recently, many different variations of these topological indices appeared in the literature and sometimes they are all together called Szeged-like topological indices. In this paper, we formally introduce the concept of a general Szeged-like topological index, which includes all mentioned indices and also infinitely many other topological indices that can be defined in a similar way. As the main result of the paper, we provide a cut method for computing a general Szeged-like topological index for any strength-weighted graph. This greatly generalizes various methods known for some of the mentioned indices and therefore rounds off such investigations. Moreover, we provide applications of our main result to benzenoid systems, phenylenes, and coronoid systems, which are well-known families of molecular graphs. In particular, closed-form formulas for some subfamilies of these graphs are deduced.