Equitable colorings of Kronecker products of graphs

For a positive integer k, a graph G is equitably k-colorable if there is a mapping f : V(G) -> {1, 2, ..., k} such that f(x) not equal f(y) whenever xy is an element of E(G) and vertical bar vertical bar f(-1) (i)vertical bar - vertical bar f(-1) (j)vertical bar vertical bar <= 1 for 1 <= i <= j <= k. The equitable chromatic number of a graph G, denoted by chi=(G), is the minimum k such that G is equitably k-colorable. The equitable chromatic threshold of a graph G, denoted by chi=(G), is the minimum t such that G is equitably k-colorable for k >= t. The current paper studies equitable chromatic numbers of Kronecker products of graphs. In particular, we give exact values or upper bounds on chi=(G x H) and chi=(G x H) when G and H are complete graphs, bipartite graphs, paths or cycles. (C) 2010 Elsevier B.V. All rights reserved.