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Wielandt type theorem for Cartesian product of digraphs
- Issue Date
- 1-8월-2008
- Publisher
- ELSEVIER SCIENCE INC
- Keywords
- exponent; Cartesian product; digraphs
- Citation
- LINEAR ALGEBRA AND ITS APPLICATIONS, v.429, no.4, pp.841 - 848
- Indexed
- SCIE
SCOPUS
- Journal Title
- LINEAR ALGEBRA AND ITS APPLICATIONS
- Volume
- 429
- Number
- 4
- Start Page
- 841
- End Page
- 848
- ISSN
- 0024-3795
- Abstract
- We show that mn - 1 is an upper bound of the exponent of the Cartesian product D x 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 x E is mn - 1. In addition, when m = n, we prove that the extremal upper bound of exp(D x E) is n(2) - n + 1 and only the Cartesian product, Z(n) x W-n, of the directed cycle and Wielandt digraph has exponent equals to this bound. (C) 2008 Elsevier Inc. All rights reserved.
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Related Researcher
- Hwang, Woon Jae
- 과학기술대학 (응용수리과학부 데이터계산과학전공)