EXTENSION OF M-POLYNOMIAL AND DEGREE BASED TOPOLOGICAL INDICES FOR NANOTUBE

The M-polynomial of a graph G(V(G),E(G)) is defined as M (G; u, v) =Sigma(i <= j) m(ij)u(i)v(j), where m(ij) denotes the number of edges xy is an element of E(G) such that {d(x), d(y)} = {i, j}, where d(x), d(y) denote degree of the vertex x and yin 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].