On Cubic Graphs Admitting an Edge-Transitive Solvable Group |
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Authors: | Aleksander Malnič Dragan Marušič Primož Potočnik |
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Institution: | (1) IMFM, Oddelek za matematiko, Univerza v Ljubljani, Jadranska 19, 1111 Ljubljana, Slovenija |
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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 K
4, 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 K
3,3, is constructed. |
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Keywords: | symmetric graph edge transitive graph cubic graph trivalent graph covering projection of graphs solvable group of automorphisms |
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