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dc.contributor.authorCameron, Peter Jephson
dc.contributor.authorSpiga, Pablo
dc.date.accessioned2015-04-03T11:01:01Z
dc.date.available2015-04-03T11:01:01Z
dc.date.issued2015-06
dc.identifier178499345
dc.identifier1c635c8a-6d90-47b7-9882-34530dec2425
dc.identifier84926380738
dc.identifier000362588300007
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.otherORCID: /0000-0003-3130-9505/work/58055528
dc.identifier.urihttps://hdl.handle.net/10023/6429
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.format.extent15
dc.format.extent150012
dc.language.isoeng
dc.relation.ispartofAustralasian Journal of Combinatoricsen
dc.subjectSwitching classesen
dc.subjectAutomorphism groupsen
dc.subjectPrimitive groupsen
dc.subjectQA Mathematicsen
dc.subjectDiscrete Mathematics and Combinatoricsen
dc.subjectAlgebra and Number Theoryen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titleMost switching classes with primitive automorphism groups contain graphs with trivial groupsen
dc.typeJournal articleen
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
dc.identifier.urlhttp://ajc.maths.uq.edu.au/pdf/62/ajc_v62_p076.pdfen


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