Geodesic
Properties of digraphs connected with some congruence relations
Czechoslovak Mathematical Journal, Tome 59 (2009) no. 1, pp. 39-49

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

The paper extends the results given by M. Křížek and L. Somer, {\it 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 $H=\{0,1,\dots ,n - 1\}$ and for which there is a directed edge from $a\in H$ to $b\in H$ if $a^3\equiv b\pmod n.$ 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.
Classification : 05C20, 05C25, 11A15, 20K01
Keywords: digraphs; Chinese remainder theorem; Carmichael $\lambda $-function; group theory 
@article{CMJ_2009__59_1_a2,
     author = {Skowronek-Kazi\'ow, J.},
     title = {Properties of digraphs connected with some congruence relations},
     journal = {Czechoslovak Mathematical Journal},
     pages = {39--49},
     publisher = {mathdoc},
     volume = {59},
     number = {1},
     year = {2009},
     mrnumber = {2486614},
     zbl = {1221.05183},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2009__59_1_a2/}
}
TY  - JOUR
AU  - Skowronek-Kaziów, J.
TI  - Properties of digraphs connected with some congruence relations
JO  - Czechoslovak Mathematical Journal
PY  - 2009
SP  - 39
EP  - 49
VL  - 59
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMJ_2009__59_1_a2/
LA  - en
ID  - CMJ_2009__59_1_a2
ER  - 
%0 Journal Article
%A Skowronek-Kaziów, J.
%T Properties of digraphs connected with some congruence relations
%J Czechoslovak Mathematical Journal
%D 2009
%P 39-49
%V 59
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMJ_2009__59_1_a2/
%G en
%F CMJ_2009__59_1_a2
Skowronek-Kaziów, J. Properties of digraphs connected with some congruence relations. Czechoslovak Mathematical Journal, Tome 59 (2009) no. 1, pp. 39-49. http://geodesic.mathdoc.fr/item/CMJ_2009__59_1_a2/