Optimal Adjacent Vertex-Distinguishing Edge-Colorings of Circulant Graphs

Abstract

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 ${\chi }_a^{\prime }(G)$. We prove that ${\chi }_a^{\prime }(G)=2R+1$ for most circulant graphs $C_n([1,R])$.

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