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dc.contributor.authorCameron, Peter Jephson
dc.contributor.authorSpiga, Pablo
dc.identifier.citationCameron , P J & Spiga , P 2015 , ' Most switching classes with primitive automorphism groups contain graphs with trivial groups ' , Australasian Journal of Combinatorics , vol. 62 , no. 1 , pp. 76-90 .en
dc.identifier.otherPURE: 178499345
dc.identifier.otherPURE UUID: 1c635c8a-6d90-47b7-9882-34530dec2425
dc.identifier.otherScopus: 84926380738
dc.identifier.otherORCID: /0000-0003-3130-9505/work/58055528
dc.identifier.otherWOS: 000362588300007
dc.description.abstractThe operation of switching a graph Gamma with respect to a subset X of the vertex set interchanges edges and non-edges between X and its complement, leaving the rest of the graph unchanged. This is an equivalence relation on the set of graphs on a given vertex set, so we can talk about the automorphism group of a switching class of graphs. It might be thought that switching classes with many automorphisms would have the property that all their graphs also have many automorphisms. But the main theorem of this paper shows a different picture: with finitely many exceptions, if a non-trivial switching class S has primitive automorphism group, then it contains a graph whose automorphism group is trivial. We also find all the exceptional switching classes; up to complementation, there are just six.
dc.relation.ispartofAustralasian Journal of Combinatoricsen
dc.rightsMade available under Diamond Open Access which is RCUK-compliant and allows immediate deposit of the version of record in repositories without restriction on re-use.en
dc.subjectSwitching classesen
dc.subjectAutomorphism groupsen
dc.subjectPrimitive groupsen
dc.subjectQA Mathematicsen
dc.subjectDiscrete Mathematics and Combinatoricsen
dc.subjectAlgebra and Number Theoryen
dc.titleMost switching classes with primitive automorphism groups contain graphs with trivial groupsen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Statisticsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.description.statusPeer revieweden

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