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

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.