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DENG Kai, LIU Xin-sheng, TIAN Shuang-liang. Star edge coloring of $d$-dimensional grids[J]. Journal of East China Normal University (Natural Sciences), 2012, (3): 13-16.
Citation:
DENG Kai, LIU Xin-sheng, TIAN Shuang-liang. Star edge coloring of $d$-dimensional grids[J]. Journal of East China Normal University (Natural Sciences), 2012, (3): 13-16.
DENG Kai, LIU Xin-sheng, TIAN Shuang-liang. Star edge coloring of $d$-dimensional grids[J]. Journal of East China Normal University (Natural Sciences), 2012, (3): 13-16.
Citation:
DENG Kai, LIU Xin-sheng, TIAN Shuang-liang. Star edge coloring of $d$-dimensional grids[J]. Journal of East China Normal University (Natural Sciences), 2012, (3): 13-16.
The star chromatic index of graph $G$ is denoted by $\chi_{s}^{\prime}(G)$. In this paper, we studied the relationship between $\chi_{s}^{\prime}(G)$, $|V(G)|=\nu$, and $|E(G)|=\varepsilon$, and proved that $\lceil\frac{8\varepsilon}{3\nu}\rceil\leqslant\chi_{s}^{\prime}(G)$ for $\Delta(G)\geqslant2$. The star chromatic index of 2-dimensional grid was obtained. We also got the attainable bounds for the star chromatic index of hypercubes and $d$-dimensional grids.