M-Polynomial of Generalized Transformation Graphs B. Basavanagoud and Goutam Veerapur

Abstract

In this paper, we show geomertric-arithmetic index (GA) can be obtained from the M-polynomial of a graph by giving a suitable operator and obtain M-polynomial of generalized transformation graph G and their complements. Furthermore, we derive some degree-based topological indices from the obtained polynomials. The topological indices play an important role in determining physico-chemical properties of chemical graphs and topological indices such as the Randic index, geomertric-arithmetic index are used to predict the bioactivity of chemical compounds, among them the degree-based topological indices can be easily driven from an algebraic expression corresponding to the chemical graphs called M-polynomial.[21] D. Vukičević, B. Furtula, Topological index based on the ratio of geometrical and arithmetical means of end-vertex degrees of edges,