Automorphism groups of circulant digraphs with applications to semigroup theory

  • João Araújo
  • Wolfram Bentz
  • Edward Dobson
  • Janusz Konieczny
  • Joy Morris
Article

Abstract

We characterize the automorphism groups of circulant digraphs whose connection sets are relatively small, and of unit circulant digraphs. For each class, we either explicitly determine the automorphism group or we show that the graph is a “normal” circulant, so the automorphism group is contained in the normalizer of a cycle. Then we use these characterizations to prove results on the automorphisms of the endomorphism monoids of those digraphs. The paper ends with a list of open problems on graphs, number theory, groups and semigroups.

Mathematics Subject Classification (2000)

05C25 20M20 20B25 

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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • João Araújo
    • 1
  • Wolfram Bentz
    • 2
  • Edward Dobson
    • 3
    • 4
  • Janusz Konieczny
    • 5
  • Joy Morris
    • 6
  1. 1.Universidade Aberta and CEMAT-Ciências Faculdade de CiênciasUniversidade de LisboaLisboaPortugal
  2. 2.School of Mathematics and Physical SciencesUniversity of HullKingston upon HullUK
  3. 3.Department of Mathematics and StatisticsMississippi State University PO Drawer MAMississippi StateUSA
  4. 4.IAMUniversity of PrimorskaKoperSlovenia
  5. 5.Department of MathematicsUniversity of Mary WashingtonFredericksburgUSA
  6. 6.Department of Math and CSUniversity of LethbridgeLethbridgeCanada

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