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  • Automorphisms of Cayley graphs on generalised dicyclic groups
    Morris, Joy ; Spiga, Pablo ; Verret, Gabriel
    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 [L. Babai and C. D. Godsil, Eur. J. Comb. 3, 9-15 (1982)]. Indeed, any Cayley graph on such a group admits specific additional graph automorphisms that depend only on the group. E. Dobson et al. ["Cayley graphs on abelian groups" (to appear)] showed that almost all Cayley graphs on abelian groups admit no automorphisms other than these obvious necessary ones. In this paper, we prove the analogous result for Cayley graphs on the remaining family of exceptional groups: generalised dicyclic groups.
    Source: European journal of combinatorics = Journal européen de combinatoire = Europäische Zeitschrift für Kombinatorik. - ISSN 0195-6698 (Vol. 43, Jan. 2015, str. 68-81)
    Type of material - article, component part ; adult, serious
    Publish date - 2015
    Language - english
    COBISS.SI-ID - 1536989380

    Link(s):

    http://www.sciencedirect.com/science/article/pii/S0195669814001024#
    DOI

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