Let G be a graph with vertex set V (G) and edge set E(G). The Nano-Zagreb and multiplicative Nano-Zagreb indicesis 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.Index Terms-Graph operations, Nano-Zagreb index, Multiplicative Nano-Zagreb index, Zagreb index.
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