On cubic graphs admitting an edge-transitive solvable group
Malnič, Aleksander ; Marušič, Dragan ; Potočnik, Primož, 1971-
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 others, that every ...such graph can be obtained from either the 3-dipole Dip▫$_3$▫ or the complete graph ▫$K_4$▫, by a sequence of elementary abelian covers. Another consequence of the main structural results is that the action of an arc-transitive solvable group on a connected cubic simple graph is at most 3-arc-transitive, and similarly, the action of an edge- but not vertex-transitive solvable group is at most 5-path-transitive. Moreover, new infinite families of semisymmetric cubic graphs are constructed, arising as regular elementary abelian covering projections of ▫$K_{3,3}$▫, the Heawood graph and the Moebius-Kantor graph.
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