The NP-completeness of authomorphic colorings
Giuseppe Mazzuoccolo · Discussiones Mathematicae Graph Theory · 2010
Given a graph G, an automorphic edge(vertex)-coloring of G is a proper edge(vertex)-coloring such that each automorphism of the graph preserves the coloring.The automorphic chromatic index (number) is the least integer k for which G admits an automorphic edge(vertex)coloring with k colors.We show that it is NP-complete to determine the automorphic chromatic index and the automorphic chromatic number of an arbitrary graph.