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 mijuivj, 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 HC5C7[p,q] and VC5C7[p,q]. © 2021