A $k$-proper edge-coloring of a graph G is called adjacent vertex-distinguishing if any two adjacent vertices are distinguished by the set of colors appearing in the edges incident to each vertex. The smallest value $k$ for which $G$ admits such coloring is denoted by $\chi'_a(G)$. We prove that $\chi'_a(G) = 2R + 1$ for most circulant graphs $C_n([1, R])$.
翻译:图形 G 的 $k$- proper 边缘颜色, 如果任何两个相邻的脊椎被每个顶端的边缘事件所显示的一组颜色所区别, 则称为相邻的顶点分色 。 $G 承认这种颜色最小值的 $k$ 以 $\ chi'_ a( G) 表示。 我们证明, $\ chi' a( G) = 2R + 1美元 用于大多数 circulan 图形 $C_n ( [ 1, R) 。