The distinguishing index $D^{\prime }\left(\Gamma \right)$ of a graph $\Gamma$ is the least number $k$ such that $\Gamma$ has an edge-coloring with $k$ colors preserved only by the trivial automorphism. In this paper we prove that if the automorphism group of a finite graph $\Gamma$ is simple, then its distinguishing index $D^{\prime }\left(\Gamma \right)=2$.

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具有简单自同构群的图的区分索引

区分指数 $D^{\prime }\left(\Gamma \right)$ 图的 $\Gamma$ 是最少的数字 $克$ 以至于 $\Gamma$ 有一个边缘着色 $克$颜色仅由平凡的自同构保留。本文证明如果有限图的自同构群$\Gamma$ 很简单，那么它的区分指标 $D^{\prime }\left(\Gamma \right)=2$.