Journal of Advances in Mathematics and Computer Science

On Multiplicative and Redefined Version of Zagreb Indices of V-Phenylenic Nanotubes and Nanotorus

Mohammad Reza Farahani *

Department of Applied Mathematics, Iran University of Science and Technology (IUST), Narmak, Tehran 16844, Iran.

Wei Gao

School of Information Science and Technology, Yunnan Normal University, Kunming 650500, China.

*Author to whom correspondence should be addressed.

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Abstract

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 d_u and d_v 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}).

Keywords: Topological index, Zagreb index, Multiple Zagreb indices, V-Phenylenic Nanotubes, V-Phenylenic Nanotorus.

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