Geodesic
Endomorphisms of functional graphs
Diskretnaya Matematika, Tome 18 (2006) no. 3, pp. 115-119 
V. A. Kolmykov. Endomorphisms of functional graphs. Diskretnaya Matematika, Tome 18 (2006) no. 3, pp. 115-119. http://geodesic.mathdoc.fr/item/DM_2006_18_3_a8/
@article{DM_2006_18_3_a8,
     author = {V. A. Kolmykov},
     title = {Endomorphisms of functional graphs},
     journal = {Diskretnaya Matematika},
     pages = {115--119},
     year = {2006},
     volume = {18},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2006_18_3_a8/}
}
TY  - JOUR
AU  - V. A. Kolmykov
TI  - Endomorphisms of functional graphs
JO  - Diskretnaya Matematika
PY  - 2006
SP  - 115
EP  - 119
VL  - 18
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/DM_2006_18_3_a8/
LA  - ru
ID  - DM_2006_18_3_a8
ER  - 
%0 Journal Article
%A V. A. Kolmykov
%T Endomorphisms of functional graphs
%J Diskretnaya Matematika
%D 2006
%P 115-119
%V 18
%N 3
%U http://geodesic.mathdoc.fr/item/DM_2006_18_3_a8/
%G ru
%F DM_2006_18_3_a8

Voir la notice de l'article provenant de la source Math-Net.Ru

A functional graph is a digraph describing the action of a function on a set. The endomorphisms of such graphs are of interest in group theory: the centraliser of an element of the semigroup of all mappings of a set into itself coincides with the set of all endomorphisms of a digraph corresponding to this element. In this study, the functional graphs with a countable set of vertices are considered. We introduce the notion of lineals and calculate the cardinality of the set of endomorphisms of functional graphs which are not lineals.

[1] Varlet J. C., “Endomorphisms and fully invariant congruences in unary algebras $\langle A;\Gamma \rangle$”, Bull. Soc. Roy. Sci. Liege, 39:11–12 (1970), 575–589 | MR | Zbl

[2] Skornyakov L. A., “Gruppovye unary”, Vestnik MGU. Matem. Mekh., 1977, no. 5, 65–69

[3] Bochkin A. M., “Unary s separativnym monoidom endomorfizmov”, Izv. vuzov, ser. matem., 1983, no. 5, 71–74 | MR

[4] Kolmykov V. A., “O sootnoshenii kommutativnosti v simmetricheskoi polugruppe”, Sib. matem. zhurn., 45:5 (2004), 1130–1135 | MR | Zbl