Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4602768 | Linear Algebra and its Applications | 2008 | 8 Pages |
Abstract
We show that mn-1 is an upper bound of the exponent of the Cartesian product D×E of two digraphs D and E on m,n vertices, respectively and we prove our upper bound is extremal when (m,n)=1. We also find all D and E when the exponent of D×E is mn-1. In addition, when m=n, we prove that the extremal upper bound of exp(D×E) is n2-n+1 and only the Cartesian product, Zn×Wn, of the directed cycle and Wielandt digraph has exponent equals to this bound.
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Physical Sciences and Engineering
Mathematics
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