Isomorphic digraphs from powers modulo $p$

Deng, Guixin, and Yuan, Pingzhi. "Isomorphic digraphs from powers modulo $p$." Czechoslovak Mathematical Journal 61.3 (2011): 771-779. <http://eudml.org/doc/196806>.

@article{Deng2011,
abstract = {Let $p$ be a prime. We assign to each positive number $k$ a digraph $G_\{p\}^\{k\}$ whose set of vertices is $\lbrace 1,2,\ldots ,p-1\rbrace $ and there exists a directed edge from a vertex $a$ to a vertex $b$ if $a^k\equiv b \hspace\{4.44443pt\}(\@mod \; p)$. In this paper we obtain a necessary and sufficient condition for $G_\{p\}^\{k_\{1\}\}\simeq G_\{p\}^\{k_\{2\}\}$.},
author = {Deng, Guixin, Yuan, Pingzhi},
journal = {Czechoslovak Mathematical Journal},
keywords = {congruence; digraph; component; height; congruence; digraph; component; height},
language = {eng},
number = {3},
pages = {771-779},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Isomorphic digraphs from powers modulo $p$},
url = {http://eudml.org/doc/196806},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Deng, Guixin
AU - Yuan, Pingzhi
TI - Isomorphic digraphs from powers modulo $p$
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 3
SP - 771
EP - 779
AB - Let $p$ be a prime. We assign to each positive number $k$ a digraph $G_{p}^{k}$ whose set of vertices is $\lbrace 1,2,\ldots ,p-1\rbrace $ and there exists a directed edge from a vertex $a$ to a vertex $b$ if $a^k\equiv b \hspace{4.44443pt}(\@mod \; p)$. In this paper we obtain a necessary and sufficient condition for $G_{p}^{k_{1}}\simeq G_{p}^{k_{2}}$.
LA - eng
KW - congruence; digraph; component; height; congruence; digraph; component; height
UR - http://eudml.org/doc/196806
ER -