Note on the multiplicative Zagreb indices

The first and second multiplicative Zagreb indices of a graph G are Π1(G)=∏v∈V(G)(d(v))2 and Π2(G)=∏uv∈E(G)d(u)d(v), respectively. Eliasi et al. (2012) introduced a multiplicative version of the first Zagreb index, defined as Π1∗(G)=∏uv∈E(G)(d(u)+d(v)) and Xu and Hua (2012) named it as the multiplicative sum Zagreb index. In this paper, we study the multiplicative Zagreb indices of molecular graphs with tree structure. More precisely, we obtain the bounds for the moments and the probability generating function of these indices in a randomly chosen molecular graph with tree structure of order n.