Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4653456 | European Journal of Combinatorics | 2015 | 11 Pages |
Abstract
A cubic graph ΓΓ is GG-arc-transitive if G≤Aut(Γ) acts transitively on the set of arcs of ΓΓ, and GG-basic if ΓΓ is GG-arc-transitive and GG has no non-trivial normal subgroup with more than two orbits. Let GG be a solvable group. In this paper, we first classify all connected GG-basic cubic graphs and determine the group structure for every GG. Then, combining covering techniques, we prove that a connected cubic GG-arc-transitive graph is either a Cayley graph, or its full automorphism group is of type 2222, that is, a 22-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 66.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Yan-Quan Feng, Cai Heng Li, Jin-Xin Zhou,