First and second multiplicative Zagreb indices and multiplicative sum Zagreb index of trees

For a graph G with vertex set V (G) and edge set E(G), the first multiplicative Zagreb index of a graph G is defined as PM1(G) = Π v∈V (G) dG(v)2, the second multiplicative Zagreb index of a graph G is defined as PM2(G) = Π uv∈E(G) dG(u)dG(v) and the multiplicative sum Zagreb index of G is defined as PM3(G) = Π uv∈E(G)[dG(u) + dG(v)], where dG(v) is the degree of vertex v in G. In this paper, we presents upper bound on first multiplicative Zagreb and lower bounds on second multiplicative Zagreb index and multiplicative sum Zagreb index in terms of maximum degree Δ.

Keywords:

First multiplicative Zagreb index , Second multiplicative Zagreb index , Multiplicative sum Zagreb