@article {
author = {Kazemi, R.},
title = {The ratio and product of the multiplicative Zagreb indices},
journal = {Iranian Journal of Mathematical Chemistry},
volume = {8},
number = {4},
pages = {377-390},
year = {2017},
publisher = {University of Kashan},
issn = {2228-6489},
eissn = {2008-9015},
doi = {10.22052/ijmc.2017.53731.1198},
abstract = {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.},
keywords = {Molecular graph with tree structure, Multiplicative Zagreb indices,Moments,Doob's supermartingale inequality},
url = {https://ijmc.kashanu.ac.ir/article_45116.html},
eprint = {https://ijmc.kashanu.ac.ir/article_45116_c080bfbf95b3706d865e19550282e4e3.pdf}
}