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A NORMAL NON-CAYLEY-INVARIANT GRAPH FOR THE ELEMENTARY ABELIAN GROUP OF ORDER 64

Part of: Graph theory

Published online by Cambridge University Press:  01 December 2008

GORDON F. ROYLE
GORDON F. ROYLE*
Affiliation:
School of Mathematics and Statistics, University of Western Australia, Nedlands, WA 6009, Australia (email: [email protected])
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Abstract

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We exhibit an interesting Cayley graph X of the elementary abelian group Z26 with the property that Aut(X) contains two regular subgroups, exactly one of which is normal. This demonstrates the existence of two subsets of Z26 that yield isomorphic Cayley graphs, even though the two subsets are not equivalent under the automorphism group of Z26.

Keywords

Cayley graphCI-graphstrongly regular graph

MSC classification

Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 85 , Issue 3 , December 2008 , pp. 347 - 351
Copyright
Copyright © Australian Mathematical Society 2009

References

[1]Frankl, P., ‘Orthogonal vectors in the n-dimensional cube and codes with missing distances’, Combinatorica 6(3) (1986), 279–285.CrossRefGoogle Scholar
[2]Godsil, C. and Royle, G., Algebraic Graph Theory, Graduate Texts in Mathematics, 207 (Springer, New York, 2001).CrossRefGoogle Scholar
[3]Ito, N., ‘Hadamard graphs. I’, Graphs Combin. 1(1) (1985), 57–64.CrossRefGoogle Scholar
[4]Ito, N., ‘Hadamard graphs. II’, Graphs Combin. 1(4) (1985), 331–337.Google Scholar
[5]Li, C. H., ‘On isomorphisms of finite Cayley graphs—a survey’, Discrete Math. 256(1–2) (2002), 301–334.CrossRefGoogle Scholar
[6]Nowitz, L. A., ‘A non-Cayley-invariant Cayley graph of the elementary abelian group of order 64’, Discrete Math. 110(1–3) (1992), 223–228.Google Scholar