Geodesic
On cubic graphs admitting an edge-transitive solvable group
Journal of Algebraic Combinatorics, Tome 20 (2004) no. 1, pp. 99-113.

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Summary: 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 Dip $_{3}$ 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.
Keywords: symmetric graph, edge transitive graph, cubic graph, trivalent graph, covering projection of graphs, solvable group of automorphisms 
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Malnič, Aleksander; Marušič, Dragan; Potočnik, Primož. On cubic graphs admitting an edge-transitive solvable group. Journal of Algebraic Combinatorics, Tome 20 (2004) no. 1, pp. 99-113. http://geodesic.mathdoc.fr/item/JAC_2004__20_1_a0/