MULTIPLE SQUARE SNAKE GRAPHS: THE M - POLYNOMIAL AND SOME DEGREE-BASED TOPOLOGICAL INDICES

Abstract

The computation of topological indices of graphs is a topic of current interest to many researchers since they are parameters which quantify the physio-chemical properties of the chemical graphs.  The concept of M - polynomial of a graph G was introduced by Emeric Deutsch and Sandi Klavzar in 2015 as an effective tool to compute a closed formula for any such index for a given family of graphs. In this paper, the M - polynomial for the class of Multiple square snake graphs M_m (C_(4,n))  is calculated, which is then utilised to find the values of many degree based topological indices. Also, as additional results, the values of these topological indices for Square snake graphs, Double square snake graphs and Triple square snake graphs, which are special cases of the Multiple square snake graphs, are also enumerated. Topological indices are used as descriptors in QSPR/QSAR models and they help predict properties such as boiling point, stability, solubility, biological activity, toxicity, etc., without the need for experimental testing. Also, by means of these numbers, instead of handling large and complicated molecular structures, chemists can work with indices that summarize structural features. This makes mathematical modeling and comparison between molecules much easier.