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.

کلیدواژه ها:

First multiplicative Zagreb index ، Second multiplicative Zagreb index ، Multiplicative sum Zagreb