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

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

*A. Rajpoot, L. Selvaganesh*

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## Abstract

The M-polynomial of a graph G(V(G),E(G)) is defined as M(G;u,v) = Ei≤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 car- bon nanotube structures, namely HC5C7[p, q] and V C5C7[p, q].

## Keywords

M-Polynomial, Carbon Nanotubes, Degree-based topological index, Graph Polynomials