On semiregular digraphs of the congruence $x^k\equiv y(modn)$

@article{Somer2007,
abstract = {We assign to each pair of positive integers $n$ and $k\ge 2$ a digraph $G(n,k)$ whose set of vertices is $H=\lbrace 0,1,\dots ,n-1\rbrace $ and for which there is a directed edge from $a\in H$ to $b\in H$ if $a^k\equiv b\hspace\{4.44443pt\}(\@mod \; n)$. The digraph $G(n,k)$ is semiregular if there exists a positive integer $d$ such that each vertex of the digraph has indegree $d$ or 0. Generalizing earlier results of the authors for the case in which $k=2$, we characterize all semiregular digraphs $G(n,k)$ when $k\ge 2$ is arbitrary.},
author = {Somer, Lawrence, Křížek, Michal},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Chinese remainder theorem; congruence; group theory; dynamical system; regular and semiregular digraphs; Chinese remainder theorem; congruence; group theory; dynamical system; regular and semiregular digraphs},
language = {eng},
number = {1},
pages = {41-58},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On semiregular digraphs of the congruence $x^k\equiv y \hspace\{4.44443pt\}(\@mod \; n)$},
url = {http://eudml.org/doc/250213},
volume = {48},
year = {2007},
}

TY - JOUR
AU - Somer, Lawrence
AU - Křížek, Michal
TI - On semiregular digraphs of the congruence $x^k\equiv y \hspace{4.44443pt}(\@mod \; n)$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2007
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 48
IS - 1
SP - 41
EP - 58
AB - We assign to each pair of positive integers $n$ and $k\ge 2$ a digraph $G(n,k)$ whose set of vertices is $H=\lbrace 0,1,\dots ,n-1\rbrace $ and for which there is a directed edge from $a\in H$ to $b\in H$ if $a^k\equiv b\hspace{4.44443pt}(\@mod \; n)$. The digraph $G(n,k)$ is semiregular if there exists a positive integer $d$ such that each vertex of the digraph has indegree $d$ or 0. Generalizing earlier results of the authors for the case in which $k=2$, we characterize all semiregular digraphs $G(n,k)$ when $k\ge 2$ is arbitrary.
LA - eng
KW - Chinese remainder theorem; congruence; group theory; dynamical system; regular and semiregular digraphs; Chinese remainder theorem; congruence; group theory; dynamical system; regular and semiregular digraphs
UR - http://eudml.org/doc/250213
ER -