Note on the multiplicative Zagreb indices

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作者：Ramin Kazemi ^{r.kazemi@SCI.ikiu.ac.ir" class="auth_mail" title="E-mail the corresponding author}
关键词：The multiplicative Zagreb indices ; Moments ; Probability generating function ; Doob&rsquo ; s supermartingale inequality
刊名：Discrete Applied Mathematics
出版年：2016
出版时间：10 January 2016
年：2016
卷：198
期：Complete
页码：147-154
全文大小：406 K

文摘

The first and second multiplicative Zagreb indices of a graph G

G

are

Π_{1} (G) = \prod_{v \in V (G)} {(d (v))}^{2}

and

Π_{2} (G) = \prod_{u v \in E (G)} d (u) d (v),

respectively. Eliasi et al. (2012) introduced a multiplicative version of the first Zagreb index, defined as

Π_{1}^{*} (G) = \prod_{u v \in 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

n

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