Geodesic
Endomorphisms of functional graphs
Diskretnaya Matematika, Tome 18 (2006) no. 3, pp. 115-119

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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. 
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     author = {V. A. Kolmykov},
     title = {Endomorphisms of functional graphs},
     journal = {Diskretnaya Matematika},
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     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2006_18_3_a8/}
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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/