Endomorphisms of graphs I. The monoid of strong endomorphisms
Copyright policy )Endomorphisms of graphs I. The monoid of strong endomorphisms
[Part II, cf. the review below.] We use the fact that every graph is a generalized lexicographic product of an S-unretractive graph with sets, to show that the monoid of strong endomorphisms of any graph is isomorphic to a wreath product of a group with a certain small category. This implies information on algebraic properties of the monoid of strong endomorphisms. In particular, it is always a regular monoid.
wreath product of a group, regular monoid, monoid of strong endomorphisms, Groupoids (i.e. small categories in which all morphisms are isomorphisms), Graphs and abstract algebra (groups, rings, fields, etc.), generalized lexicographic product
wreath product of a group, regular monoid, monoid of strong endomorphisms, Groupoids (i.e. small categories in which all morphisms are isomorphisms), Graphs and abstract algebra (groups, rings, fields, etc.), generalized lexicographic product
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