%0 Journal Article
%T The Ratio and Product of the Multiplicative Zagreb Indices
%J Iranian Journal of Mathematical Chemistry
%I University of Kashan
%Z 2228-6489
%A Kazemi, R.
%D 2017
%\ 12/01/2017
%V 8
%N 4
%P 377-390
%! The Ratio and Product of the Multiplicative Zagreb Indices
%K Molecular graph with tree structure, Multiplicative Zagreb indices
%K Moments
%K Doob's supermartingale inequality
%R 10.22052/ijmc.2017.53731.1198
%X The first multiplicative Zagreb index $\Pi_1(G)$ is equal to the product of squares of the degree of the vertices and the second multiplicative Zagreb index $\Pi_2(G)$ is equal to the product of the products of the degree of pairs of adjacent vertices of the underlying molecular graphs $G$. Also, the multiplicative sum Zagreb index $\Pi_3(G)$ is equal to the product of the sums of the degree of pairs of adjacent vertices of $G$. In this paper, we introduce a new version of the multiplicative sum Zagreb index and study the moments of the ratio and product of all above indices in a randomly chosen molecular graph with tree structure of order $n$. Also, a supermartingale is introduced by Doob's supermartingale inequality.
%U https://ijmc.kashanu.ac.ir/article_45116_c080bfbf95b3706d865e19550282e4e3.pdf