TY - JOUR
ID - 4988
TI - Multiplicative Zagreb eccentricity indices of some composite graphs
JO - Transactions on Combinatorics
JA - TOC
LA - en
SN - 2251-8657
AU - Luo, Zhaoyang
AU - Wu, Jianliang
AD - B913, Zhixin Building
School of Mathematics
Shandong University
27 Shandananlu Rd.
AD - School of Mathematics, Shandong University
Y1 - 2014
PY - 2014
VL - 3
IS - 2
SP - 21
EP - 29
KW - Multiplicative Zagreb eccentricity indices
KW - composite operations
KW - Cartesian product
DO - 10.22108/toc.2014.4988
N2 - 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.
UR - https://toc.ui.ac.ir/article_4988.html
L1 - https://toc.ui.ac.ir/article_4988_b31eb90142535e6abd5d71fbd403678a.pdf
ER -