| 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:
|
2020-07-03 |
| 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 |
| . |
