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 etal., in press). In this paper, we prove the analogous result for Cayley graphs on the remaining family of exceptional groups: generalised dicyclic groups. © 2014 Elsevier Ltd.

Morris, J., Spiga, P., Verret, G. (2015). Automorphisms of Cayley graphs on generalised dicyclic groups. EUROPEAN JOURNAL OF COMBINATORICS, 43, 68-81 [10.1016/j.ejc.2014.07.003].

Automorphisms of Cayley graphs on generalised dicyclic groups

SPIGA, PABLO
Secondo
;
2015

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 etal., in press). In this paper, we prove the analogous result for Cayley graphs on the remaining family of exceptional groups: generalised dicyclic groups. © 2014 Elsevier Ltd.
Articolo in rivista - Articolo scientifico
Geometry and Topology; Theoretical Computer Science; Computational Theory and Mathematics; Discrete Mathematics and Combinatorics
English
68
81
14
Morris, J., Spiga, P., Verret, G. (2015). Automorphisms of Cayley graphs on generalised dicyclic groups. EUROPEAN JOURNAL OF COMBINATORICS, 43, 68-81 [10.1016/j.ejc.2014.07.003].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/133245
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