LAUSR

Let G be a simple graph with vertex set V(G) and edge set E(G). In [7], Eliasi et al. introduced the multiplicative sum Zagreb index of a graph G which is denoted by Π1(G) and is defined by Π1(G) = ∏ uv∈V (G) (dG(u)+dG(v)) . In this paper, we present some upper bounds for the multiplicative sum Zagreb indices of the join, rooted product, corona product, tensor product, Cartesian product, strong product, hierarchical product, lexicographic product of graphs. Mathematics subject classification (2010): 05C35, 05C76, 05C07.