On Cubic Graphs Admitting an Edge-Transitive Solvable Group

  • Authors:

  • Aleksander Malnič;Dragan Marušič;Primož Potočnik

  • Affiliations:

  • IMFM, Oddelek za matematiko, Univerza v Ljubljani, Jadranska 19, 1111 Ljubljana, Slovenija;IMFM, Oddelek za matematiko, Univerza v Ljubljani, Jadranska 19, 1111 Ljubljana, Slovenija;IMFM, Oddelek za matematiko, Univerza v Ljubljani, Jadranska 19, 1111 Ljubljana, Slovenija

  • Venue:
  • Journal of Algebraic Combinatorics: An International Journal
  • Year:
  • 2004

Quantified Score

Hi-index 0.00

Visualization

Abstract

Using covering graph techniques, a structural result about connected cubic simple graphs admitting an edge-transitive solvable group of automorphisms is proved. This implies, among other, that every such graph can be obtained from either the 3-dipole Dip3 or the complete graph K4, by a sequence of elementary-abelian covers. Another consequence of the main structural result is that the action of an arc-transitive solvable group on a connected cubic simple graph is at most 3-arc-transitive. As an application, a new infinite family of semisymmetric cubic graphs, arising as regular elementary abelian covering projections of K3,3, is constructed.