Upper Bounds for the Modified Second Multiplicative Zagreb Index of Graph Operations

Abstract

The modified second multiplicative Zagreb index of a connected graph G, denoted by ∏ ‍ 2 (G), is defined as ∏ ‍ ∗ 2 (G) = ∏ ‍ uv∈E(G) [dG(u) + dG(v)] [dG(u)+dG(v)] where dG(z) is the degree of a vertex z in G . In this paper, we present some upper bounds for the modified second multiplicative Zagreb index of graph operations such as union, join, Cartesian product, composition and corona product of graphs are derived.