Geodesic
On a connection of number theory with graph theory
Czechoslovak Mathematical Journal, Tome 54 (2004) no. 2, pp. 465-485.

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

We assign to each positive integer $n$ a digraph 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 $a^2\equiv b\hspace{4.44443pt}(\@mod \; n)$. We establish necessary and sufficient conditions for the existence of isolated fixed points. We also examine when the digraph is semiregular. Moreover, we present simple conditions for the number of components and length of cycles. Two new necessary and sufficient conditions for the compositeness of Fermat numbers are also introduced.
Classification : 05C20, 11A07, 11A15, 11A51, 20K01
Keywords: Fermat numbers; Chinese remainder theorem; primality; group theory; digraphs 
@article{CMJ_2004__54_2_a18,
     author = {Somer, Lawrence and K\v{r}{\'\i}\v{z}ek, Michal},
     title = {On a connection of number theory with graph theory},
     journal = {Czechoslovak Mathematical Journal},
     pages = {465--485},
     publisher = {mathdoc},
     volume = {54},
     number = {2},
     year = {2004},
     mrnumber = {2059267},
     zbl = {1080.11004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2004__54_2_a18/}
}
TY  - JOUR
AU  - Somer, Lawrence
AU  - Křížek, Michal
TI  - On a connection of number theory with graph theory
JO  - Czechoslovak Mathematical Journal
PY  - 2004
SP  - 465
EP  - 485
VL  - 54
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMJ_2004__54_2_a18/
LA  - en
ID  - CMJ_2004__54_2_a18
ER  - 
%0 Journal Article
%A Somer, Lawrence
%A Křížek, Michal
%T On a connection of number theory with graph theory
%J Czechoslovak Mathematical Journal
%D 2004
%P 465-485
%V 54
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMJ_2004__54_2_a18/
%G en
%F CMJ_2004__54_2_a18
Somer, Lawrence; Křížek, Michal. On a connection of number theory with graph theory. Czechoslovak Mathematical Journal, Tome 54 (2004) no. 2, pp. 465-485. http://geodesic.mathdoc.fr/item/CMJ_2004__54_2_a18/