Optimal Adjacent Vertex-Distinguishing Edge-Colorings of Circulant Graphs [article]

Sylvain Gravier, Souad Slimani
2022 arXiv   pre-print
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]).
arXiv:2004.12822v4 fatcat:bjnfyoej7vh43jwidiwtnma3vm