The $M$-Polynomial and Topological Indices of Generalized M\"obius Ladder and Its Line Graph

TL;DR

This paper derives closed-form expressions for the $M$-polynomial of generalized M"obius ladders and their line graphs, enabling straightforward calculation of various degree-based topological indices relevant in chemistry.

Contribution

It provides the first comprehensive formulas for the $M$-polynomial of these graphs and computes multiple indices using this polynomial, advancing graph-theoretic methods in chemical graph theory.

Findings

Closed-form $M$-polynomials for generalized M"obius ladders and their line graphs.

Explicit formulas for Zagreb, Randić, and symmetric division indices.

Facilitates easier computation of topological indices in chemical graph analysis.

Abstract

The $M$-polynomial was introduced by Deutsch and Klav\v{z}ar in 2015 as a graph polynomial to provide an easy way to find closed formulas of degree-based topological indices, which are used to predict physical, chemical, and pharmacological properties of organic molecules. In this paper we give general closed forms of the $M$-polynomial of the generalized M\"obius ladder and its line graph. We also compute Zagreb Indices, generalized Randi\'c indices, and symmetric division index of these graphs via the $M$-polynomial.