Luo, Z., Wu, J. (2014). Multiplicative Zagreb eccentricity indices of some composite graphs. Transactions on Combinatorics, 3(2), 21-29. doi: 10.22108/toc.2014.4988

Zhaoyang Luo; Jianliang Wu. "Multiplicative Zagreb eccentricity indices of some composite graphs". Transactions on Combinatorics, 3, 2, 2014, 21-29. doi: 10.22108/toc.2014.4988

Luo, Z., Wu, J. (2014). 'Multiplicative Zagreb eccentricity indices of some composite graphs', Transactions on Combinatorics, 3(2), pp. 21-29. doi: 10.22108/toc.2014.4988

Luo, Z., Wu, J. Multiplicative Zagreb eccentricity indices of some composite graphs. Transactions on Combinatorics, 2014; 3(2): 21-29. doi: 10.22108/toc.2014.4988

Multiplicative Zagreb eccentricity indices of some composite graphs

^{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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