# Article

 Title: Isomorphic digraphs from powers modulo $p$ (English) Author: Deng, Guixin Author: Yuan, Pingzhi Language: English Journal: Czechoslovak Mathematical Journal ISSN: 0011-4642 (print) ISSN: 1572-9141 (online) Volume: 61 Issue: 3 Year: 2011 Pages: 771-779 Summary lang: English . Category: math . 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 $G_{p}^{k_{1}}\simeq G_{p}^{k_{2}}$. (English) Keyword: congruence Keyword: digraph Keyword: component Keyword: height MSC: 05C20 MSC: 05C38 MSC: 11A15 idZBL: Zbl 1249.05162 idMR: MR2853090 DOI: 10.1007/s10587-011-0025-y . Date available: 2011-09-22T14:45:37Z Last updated: 2016-04-07 Stable URL: http://hdl.handle.net/10338.dmlcz/141637 . 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. MR 2510326, 10.1016/j.disc.2008.04.009 .

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