On Multiplicative and Redefined Version of Zagreb Indices of V-Phenylenic Nanotubes and Nanotorus
Mohammad Reza Farahani, Wei Gao
Journal of Advances in Mathematics and Computer Science · pp. 1–8 · Published 29 Dec 2015
10.9734/BJMCS/2016/22752Abstract
Let G be an arbitrary simple and connected graph, with the vertex set V(G) and edge set E(G). The first Zagreb index of a graph G is defined as , where du and dv are the degrees of u and v, respectively. An alternative expression for M1 (G) is . And similarly, the Second Zagreb index M2 (G) = . In this paper, we consider a multiplicative version of M1 (G) and M2 (G) and define them as PM1 (G) = and PM2 (G) = , respectively. And then we compute these Multiple Zagreb indices of V-Phenylenic Nanotubes VPHX[p,q] and V-Phenylenic Nanotorus VPHY[p,q] ("p,qÎℕ-{1}). Furthermore, we present the redefined Zagreb indices of V-Phenylenic Nanotubes VPHX[p,q] and V-Phenylenic Nanotorus VPHY[p,q] ("p,qÎℕ-{1}).
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