TY - JOUR

T1 - Symmetric cubic graphs with solvable automorphism groups

AU - Feng, Y.

AU - Li, Cai-Heng

AU - Zhou, J.

PY - 2015

Y1 - 2015

N2 - © 2014 Elsevier Ltd. A cubic graph Γ is G-arc-transitive if G≤Aut(Γ) acts transitively on the set of arcs of Γ, and G-basic if Γ is G-arc-transitive and G has no non-trivial normal subgroup with more than two orbits. Let G be a solvable group. In this paper, we first classify all connected G-basic cubic graphs and determine the group structure for every G. Then, combining covering techniques, we prove that a connected cubic G-arc-transitive graph is either a Cayley graph, or its full automorphism group is of type 22, that is, a 2-regular group with no involution reversing an edge, and has a non-abelian normal subgroup such that the corresponding quotient graph is the complete bipartite graph of order 6.

AB - © 2014 Elsevier Ltd. A cubic graph Γ is G-arc-transitive if G≤Aut(Γ) acts transitively on the set of arcs of Γ, and G-basic if Γ is G-arc-transitive and G has no non-trivial normal subgroup with more than two orbits. Let G be a solvable group. In this paper, we first classify all connected G-basic cubic graphs and determine the group structure for every G. Then, combining covering techniques, we prove that a connected cubic G-arc-transitive graph is either a Cayley graph, or its full automorphism group is of type 22, that is, a 2-regular group with no involution reversing an edge, and has a non-abelian normal subgroup such that the corresponding quotient graph is the complete bipartite graph of order 6.

U2 - 10.1016/j.ejc.2014.10.008

DO - 10.1016/j.ejc.2014.10.008

M3 - Article

VL - 45

SP - 1

EP - 11

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

SN - 0195-6698

ER -