Optimal Adjacent Vertex-Distinguishing Edge-Colorings of Circulant Graphs

04/27/2020

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by   Sylvain Gravier, et al.

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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 χ'_a(G). We prove that χ'_a(G) = 2R + 1 for most circulant graphs C_n([1, R]).