Extension of m-polynomial and degree based topological indices for nanotube

Abstract

The M-polynomial of a graph G(V (G), E(G)) is defined as M(G; u, v) = ? i?j miju?v?, where mij denotes the number of edges xy ? E(G) such that {dx, dy} = {i, j}, where dx, dy denote degree of the vertex x and y in the graph G(V (G), E(G)). In this paper, we show how to compute the degree-based indices such as Forgotten index, Reduced Second Zagreb index, Sigma index, Hyper-Zagreb index and Albertson index using the M-polynomial. In addition, we present as an application how to quickly and effectively compute the degree-based topological indices using M-polynomial for two carbon nanotube structures, namely HC?C?[p, q] and VC?C?[p, q].