The structure of digraphs associated with the congruence $x^k\equiv y(modn)$

Somer, Lawrence, and Křížek, Michal. "The structure of digraphs associated with the congruence $x^k\equiv y \hspace{4.44443pt}(\@mod \; n)$." Czechoslovak Mathematical Journal 61.2 (2011): 337-358. <http://eudml.org/doc/196799>.

@article{Somer2011,
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 $a^k\equiv b\hspace\{4.44443pt\}(\@mod \; n)$. We investigate the structure of $G(n,k)$. In particular, upper bounds are given for the longest cycle in $G(n,k)$. We find subdigraphs of $G(n,k)$, called fundamental constituents of $G(n,k)$, for which all trees attached to cycle vertices are isomorphic.},
author = {Somer, Lawrence, Křížek, Michal},
journal = {Czechoslovak Mathematical Journal},
keywords = {Sophie Germain primes; Fermat primes; primitive roots; Chinese Remainder Theorem; congruence; digraphs; Sophie Germain prime; Fermat prime; primitive root; Chinese Remainder Theorem; congruence; digraph},
language = {eng},
number = {2},
pages = {337-358},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The structure of digraphs associated with the congruence $x^k\equiv y \hspace\{4.44443pt\}(\@mod \; n)$},
url = {http://eudml.org/doc/196799},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Somer, Lawrence
AU - Křížek, Michal
TI - The structure of digraphs associated with the congruence $x^k\equiv y \hspace{4.44443pt}(\@mod \; n)$
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 2
SP - 337
EP - 358
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 $a^k\equiv b\hspace{4.44443pt}(\@mod \; n)$. We investigate the structure of $G(n,k)$. In particular, upper bounds are given for the longest cycle in $G(n,k)$. We find subdigraphs of $G(n,k)$, called fundamental constituents of $G(n,k)$, for which all trees attached to cycle vertices are isomorphic.
LA - eng
KW - Sophie Germain primes; Fermat primes; primitive roots; Chinese Remainder Theorem; congruence; digraphs; Sophie Germain prime; Fermat prime; primitive root; Chinese Remainder Theorem; congruence; digraph
UR - http://eudml.org/doc/196799
ER -