On Cubic Graphs Admitting an Edge-Transitive Solvable Group
نویسندگان
چکیده
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.
منابع مشابه
Edge-colourings of cubic graphs admitting a solvable vertex-transitive group of automorphisms
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