University of IsfahanTransactions on Combinatorics2251-86573220140601Multiplicative Zagreb eccentricity indices of some composite graphs2129498810.22108/toc.2014.4988ENZhaoyangLuoB913, Zhixin Building
School of Mathematics
Shandong University
27 Shandananlu Rd.JianliangWuSchool of Mathematics, Shandong UniversityJournal Article20131018Let $G$ be a connected graph. The multiplicative Zagreb eccentricity indices of $G$ are defined respectively as ${\bf \Pi}_1^*(G)=\prod_{v\in V(G)}\varepsilon_G^2(v)$ and ${\bf \Pi}_2^*(G)=\prod_{uv\in E(G)}\varepsilon_G(u)\varepsilon_G(v)$, 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.https://toc.ui.ac.ir/article_4988_b31eb90142535e6abd5d71fbd403678a.pdf