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Most switching classes with primitive automorphism groups contain graphs with trivial groups

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cameron_spiga.pdf (146.4Kb)
Date
06/2015
Author
Cameron, Peter Jephson
Spiga, Pablo
Keywords
Switching classes
Automorphism groups
Primitive groups
QA Mathematics
Discrete Mathematics and Combinatorics
Algebra and Number Theory
T-NDAS
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Abstract
The 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.
Citation
Cameron , 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 .
Publication
Australasian Journal of Combinatorics
Status
Peer reviewed
Type
Journal article
Rights
Made 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.
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  • University of St Andrews Research
URL
http://ajc.maths.uq.edu.au/pdf/62/ajc_v62_p076.pdf
URI
http://hdl.handle.net/10023/6429

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