The praeger-xu graphs: Cycle structures, maps, and semitransitive orientations

R. Jajcay, P. Potočnik, S. Wilson

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We consider tetravalent graphs within a family introduced by Praeger and Xu in 1989. These graphs have the property of having exceptionally large symmetry groups among all tetravalent graphs. This very property makes them unsuitable for the use of simple computer techniques. We apply techniques from coding theory to determine for which values of the parameters the graphs allow cycle structures, semitransitive orientations, or rotary maps; all without recourse to the use of computers.

Original languageEnglish (US)
Pages (from-to)269-291
Number of pages23
JournalActa Mathematica Universitatis Comenianae
Issue number2
StatePublished - Jun 26 2019


  • Cycle structure
  • Graph
  • Reflexible
  • Regular map
  • Rotary map
  • Semitransitive
  • Transitive

ASJC Scopus subject areas

  • General Mathematics


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