The exponent of Cartesian product of cycles

초록

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 fora primitive graph G and a strongly connected bipartite digraph D, the exponent of the Cartesian product G x 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. (C) 2008 Elsevier Ltd. All rights reserved.

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