Multiplicative Zagreb eccentricity indices of some composite graphs

Document Type: Research Paper

Authors

1 B913, Zhixin Building School of Mathematics Shandong University 27 Shandananlu Rd.

2 School of Mathematics, Shandong University

Abstract

Let $G$ 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.

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