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Groups fixing graphas in switching classes

Part of: Graph theory

Published online by Cambridge University Press:  09 April 2009

Martin W. Liebeck
Martin W. Liebeck
Affiliation:
Department of Pure Mathematics University CollegeP.O. Box 78 Cardiff CFI 1XL Wales
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Abstract

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A permutation group G on a finite set Ω is always exposable if whenever G stabilises a switching class of graphs on Ω, G fixes a graph in the switching class. Here we consider the problem: given a finite group G, which permutation representations of G are always exposable? We present solutions to the problem for (i) 2-generator abelian groups, (ii) all abelian groups in semiregular representations. (iii) generalised quaternion groups and (iv) some representations of the symmetric group Sn.

MSC classification

Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 33 , Issue 1 , August 1982 , pp. 76 - 85
Copyright
Copyright © Australian Mathematical Society 1982

References

Cameron, P. J. (1977), ‘Cohomological aspects of two-graphs’, Math. Z. 157, 101–119.CrossRefGoogle Scholar
Harries, D. and Liebeck, H. (1978), ‘Isomorphisms in switching classes of graphs’. J. Austral. Math. Soc. Ser. A 26, 475–486.CrossRefGoogle Scholar
Mallows, C. L. and Sloane, N. J. A. (1975), ‘Two-graphs, switching classes and Euler graphs are equal in number’, SIAM J. Appl. Math. 28, 876–880.CrossRefGoogle Scholar