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 χ a (G).We prove that χ a (G) = 2R + 1 for most circulant graphs C n ([[1, R]]).