On quartic half-arc-transitive metacirculants

  • Authors:

  • Dragan Marušič;Primož Šparl

  • Affiliations:

  • FAMNIT, University of Primorska, Koper, Slovenia 6000 and IMFM, University of Ljubljana, Ljubljana, Slovenia 1111;IMFM, University of Ljubljana, Ljubljana, Slovenia 1111

  • Venue:
  • Journal of Algebraic Combinatorics: An International Journal
  • Year:
  • 2008

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Abstract

Following Alspach and Parsons, a metacirculant graph is a graph admitting a transitive group generated by two automorphisms 驴 and 驴, where 驴 is (m,n)-semiregular for some integers m驴1, n驴2, and where 驴 normalizes 驴, cyclically permuting the orbits of 驴 in such a way that 驴 m has at least one fixed vertex. A half-arc-transitive graph is a vertex- and edge- but not arc-transitive graph. In this article quartic half-arc-transitive metacirculants are explored and their connection to the so called tightly attached quartic half-arc-transitive graphs is explored. It is shown that there are three essentially different possibilities for a quartic half-arc-transitive metacirculant which is not tightly attached to exist. These graphs are extensively studied and some infinite families of such graphs are constructed.