Abstract: A vertex reducible edge coloring of a graph G is an improper edge (total) coloring such that any two vertices with identical degree have the same color set. Based on the structural characters of the generalized Petersen graph G(n,k), we use combinatorial analysis method and constructive function method to give the vertex reducible edge (total) chromatic number of G(n,k) when its order is sufficiently large.

Key words: generalized Petersen graph, vertex reducible edge coloring, vertex reducible total coloring