Ukrainian Mathematical Journal

, Volume 65, Issue 6, pp 823–834 | Cite as

Semigroups of Strong Endomorphisms of Infinite Graphs and Hypergraphs

  • E. A. Bondar’
  • Yu. V. Zhuchok
Article
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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.

Keywords

Undirected Graph Cayley Graph Semigroup Forum Wreath Product Multiple Edge 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • E. A. Bondar’
    • 1
  • Yu. V. Zhuchok
    • 1
  1. 1.Shevchenko Lugansk National UniversityLuganskUkraine

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