Nano-Zagreb Index and Multiplicative Nano-Zagreb Index of Some Graph Operations

Akbar Jahanbani (Department of Mathematics, Shahrood University of Technology)
Hajar Shooshtary (Department of Mathematics, Esfahan University of Technology)

International Journal of Computing Science and Applied Mathematics-IJCSAM
Vol. 5 No. 1 (2019)

Let G be a graph with vertex set V(G) and edge set E(G). The Nano-Zagreb and multiplicative Nano-Zagreb indices of G are NZ(G) = \prod_{uv \in E(G)} (d^2(u) - d^2(v)) and N*Z(G) = \prod_{uv \in E(G)} (d^2(u) - d^2(v)), respectively, where d(v) is the degree of the vertex v. In this paper, we define two types of Zagreb indices based on degrees of vertices. Also the Nano-Zagreb index and multiplicative Nano-Zagreb index of the Cartesian product, symmetric difference, composition and disjunction of graphs are computed.