Article
| 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 |
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| Date available: | 2011-09-22T14:45:37Z |
| Last updated: | 2012-05-31 |
| 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 |
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