About generation of non-isomorphic vertex $k$-colorings

In this paper, we study the generation problem for non-isomorphic vertex and edge $k$-colorings of a given graph. An algorithm for generating all the non-isomorphic vertex $k$-colorings of a graph by the Reed–Faradzhev method without using an isomorphism testing technique is suggested. The problem of generating edge $k$-colorings is reduced to the problem of generating vertex $k$-colorings.