Properties of digraphs connected with some congruence relations

Skowronek-Kaziów, J.. "Properties of digraphs connected with some congruence relations." Czechoslovak Mathematical Journal 59.1 (2009): 39-49. <http://eudml.org/doc/37906>.

@article{Skowronek2009,
abstract = {The paper extends the results given by M. Křížek and L. Somer, On a connection of number theory with graph theory, Czech. Math. J. 54 (129) (2004), 465–485 (see [5]). For each positive integer $n$ define a digraph $\Gamma (n)$ whose set of vertices is the set $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 $a^3\equiv b\hspace\{4.44443pt\}(\@mod \; n).$ The properties of such digraphs are considered. The necessary and the sufficient condition for the symmetry of a digraph $\Gamma (n)$ is proved. The formula for the number of fixed points of $\Gamma (n)$ is established. Moreover, some connection of the length of cycles with the Carmichael $\lambda $-function is presented.},
author = {Skowronek-Kaziów, J.},
journal = {Czechoslovak Mathematical Journal},
keywords = {digraphs; Chinese remainder theorem; Carmichael $\lambda $-function; group theory; digraph; Chinese remainder theorem; Carmichael -function; group theory},
language = {eng},
number = {1},
pages = {39-49},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Properties of digraphs connected with some congruence relations},
url = {http://eudml.org/doc/37906},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Skowronek-Kaziów, J.
TI - Properties of digraphs connected with some congruence relations
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 1
SP - 39
EP - 49
AB - The paper extends the results given by M. Křížek and L. Somer, On a connection of number theory with graph theory, Czech. Math. J. 54 (129) (2004), 465–485 (see [5]). For each positive integer $n$ define a digraph $\Gamma (n)$ whose set of vertices is the set $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 $a^3\equiv b\hspace{4.44443pt}(\@mod \; n).$ The properties of such digraphs are considered. The necessary and the sufficient condition for the symmetry of a digraph $\Gamma (n)$ is proved. The formula for the number of fixed points of $\Gamma (n)$ is established. Moreover, some connection of the length of cycles with the Carmichael $\lambda $-function is presented.
LA - eng
KW - digraphs; Chinese remainder theorem; Carmichael $\lambda $-function; group theory; digraph; Chinese remainder theorem; Carmichael -function; group theory
UR - http://eudml.org/doc/37906
ER -