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
SN - 0195-6698
VL - 45
SP - 1
EP - 11
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
ER -