Kazemi, R. (2017). The ratio and product of the multiplicative Zagreb indices. Iranian Journal of Mathematical Chemistry, 8(4), 377-390. doi: 10.22052/ijmc.2017.53731.1198

R. Kazemi. "The ratio and product of the multiplicative Zagreb indices". Iranian Journal of Mathematical Chemistry, 8, 4, 2017, 377-390. doi: 10.22052/ijmc.2017.53731.1198

Kazemi, R. (2017). 'The ratio and product of the multiplicative Zagreb indices', Iranian Journal of Mathematical Chemistry, 8(4), pp. 377-390. doi: 10.22052/ijmc.2017.53731.1198

Kazemi, R. The ratio and product of the multiplicative Zagreb indices. Iranian Journal of Mathematical Chemistry, 2017; 8(4): 377-390. doi: 10.22052/ijmc.2017.53731.1198

The ratio and product of the multiplicative Zagreb indices

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.