%0 Journal Article
%T Multiplicative Zagreb eccentricity indices of some composite graphs
%J Transactions on Combinatorics
%I University of Isfahan
%Z 2251-8657
%A Luo, Zhaoyang
%A Wu, Jianliang
%D 2014
%\ 06/01/2014
%V 3
%N 2
%P 21-29
%! Multiplicative Zagreb eccentricity indices of some composite graphs
%K Multiplicative Zagreb eccentricity indices
%K composite operations
%K Cartesian product
%R 10.22108/toc.2014.4988
%X Let $G$ be a connected graph. The multiplicative Zagreb eccentricity indices of $G$ are defined respectively as ${bf Pi}_1^*(G)=prod_{vin V(G)}varepsilon_G^2(v)$ and ${bf Pi}_2^*(G)=prod_{uvin E(G)}varepsilon_G(u)varepsilon_G(v)$, where $varepsilon_G(v)$ is the eccentricity of vertex $v$ in graph $G$ and $varepsilon_G^2(v)=(varepsilon_G(v))^2$. In this paper, we present some bounds of the multiplicative Zagreb eccentricity indices of Cartesian product graphs by means of some invariants of the factors and supply some exact expressions of ${bf Pi}_1^*$ and ${bf Pi}_2^*$ indices of some composite graphs, such as the join, disjunction, symmetric difference and composition of graphs, respectively.
%U https://toc.ui.ac.ir/article_4988_b31eb90142535e6abd5d71fbd403678a.pdf