We define a class of infinite undirected graphs and a class of infinite n-regular hypergraphs and prove that any semigroup of all strong endomorphisms of the graphs and hypergraphs from these classes is isomorphic to the wreath product of a transformation monoid and a small category. We establish the criterional conditions for the regularity of the semigroup of strong endomorphisms of infinite n-regular hypergraphs.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 6, pp. 743–754, June, 2013.
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Bondar’, E.A., Zhuchok, Y.V. Semigroups of Strong Endomorphisms of Infinite Graphs and Hypergraphs. Ukr Math J 65, 823–834 (2013). https://doi.org/10.1007/s11253-013-0820-8
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DOI: https://doi.org/10.1007/s11253-013-0820-8