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Title: Isomorphic digraphs from powers modulo $p$  (English)
Author: Deng, Guixin
Author: Yuan, Pingzhi
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642
Volume: 61
Issue: 3
Year: 2011
Pages: 771-779
Summary lang: English
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Category: math
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Summary: Let $p$ be a prime. We assign to each positive number $k$ a digraph $G_{p}^{k}$ whose set of vertices is $\{1,2,\ldots ,p-1\}$ and there exists a directed edge from a vertex $a$ to a vertex $b$ if $a^k\equiv b \pmod {p}$. In this paper we obtain a necessary and sufficient condition for $G_{p}^{k_{1}}\simeq G_{p}^{k_{2}}$.
Keyword: congruence
Keyword: digraph
Keyword: component
Keyword: height
MSC: 05C20
MSC: 05C38
MSC: 11A15
idZBL: Zbl 1249.05162
idMR: MR2853090
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Date available: 2011-09-22T14:45:37Z
Last updated: 2013-10-14
Stable URL: http://hdl.handle.net/10338.dmlcz/141637
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Reference: [1] Lucheta, C., Miller, E., Reiter, C.: Digraphs from powers modulo $p$.Fibonacci Quart. 34 (1996), 226-239. Zbl 0855.05067, MR 1390409
Reference: [2] Somer, L., Křížek, M.: On symmetric digraphs of the congruence $x^k\equiv y\pmod{n}$.Discrete Math. 309 (2009), 1999-2009. Zbl 1208.05041, MR 2510326, 10.1016/j.disc.2008.04.009
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