A census of semisymmetric cubic graphs on up to 768 vertices

  • Authors:

  • Marston Conder;Aleksander Malnič;Dragan Marušič;Primž Potočnik

  • Affiliations:

  • Department of Mathematics, University of Auckland, Auckland, New Zealand;IMFM, Oddelek za matematiko, Univerza v Ljubljani, Ljubljana, Slovenija 1111;IMFM, Oddelek za matematiko, Univerza v Ljubljani, Ljubljana, Slovenija 1111;University of Primorska, Koper, Slovenia 6000

  • Venue:
  • Journal of Algebraic Combinatorics: An International Journal
  • Year:
  • 2006

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Abstract

A list is given of all semisymmetric (edge- but not vertex-transitive) connected finite cubic graphs of order up to 768. This list was determined by the authors using Goldschmidt's classification of finite primitive amalgams of index (3,3), and a computer algorithm for finding all normal subgroups of up to a given index in a finitely-presented group. The list includes several previously undiscovered graphs. For each graph in the list, a significant amount of information is provided, including its girth and diameter, the order of its automorphism group, the order and structure of a minimal edge-transitive group of automorphisms, its Goldschmidt type, stabiliser partitions, and other details about its quotients and covers. A summary of all known infinite families of semisymmetric cubic graphs is also given, together with explicit rules for their construction, and members of the list are identified with these. The special case of those graphs having K1,3 as a normal quotient is investigated in detail.