Equitable colorings of Kronecker products of graphs

For a positive integer kk, a graph GG is equitably kk-colorable if there is a mapping f:V(G)→{1,2,…,k}f:V(G)→{1,2,…,k} such that f(x)≠f(y)f(x)≠f(y) whenever xy∈E(G)xy∈E(G) and ||f−1(i)|−|f−1(j)||≤1||f−1(i)|−|f−1(j)||≤1 for 1≤i