The exponent of Cartesian product of cycles

A digraph D is primitive if for each pair of vertices v , w of D , there is a positive integer k such that there is a directed walk of length k from v to w . The minimum of such k is the exponent of D . In this paper, we show that for a primitive graph G and a strongly connected bipartite digraph D , the exponent of the Cartesian product G × D is equal to the addition of the exponent of G and the diameter of D . Finally, we find the exponents of Cartesian products of cycles.