Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4653380 | European Journal of Combinatorics | 2015 | 14 Pages |
Abstract
A graph is called a GRR if its automorphism group acts regularly on its vertex-set. Such a graph is necessarily a Cayley graph. Godsil has shown that there are only two infinite families of finite groups that do not admit GRRs: abelian groups and generalised dicyclic groups (Babai and Godsil, 1982). Indeed, any Cayley graph on such a group admits specific additional graph automorphisms that depend only on the group. Recently, Dobson and the last two authors showed that almost all Cayley graphs on abelian groups admit no automorphisms other than these obvious necessary ones (Dobson et al., in press). In this paper, we prove the analogous result for Cayley graphs on the remaining family of exceptional groups: generalised dicyclic groups.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Joy Morris, Pablo Spiga, Gabriel Verret,