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A normal non-Cayley-invariant graph for the elementary abelian group of order 64. (English) Zbl 1167.05035

Summary: We exhibit an interesting Cayley graph \(X\) of the elementary abelian group \(Z_2^6\) with the property that Aut\((X)\) contains two regular subgroups, exactly one of which is normal. This demonstrates the existence of two subsets of \(Z_2^6\) that yield isomorphic Cayley graphs, even though the two subsets are not equivalent under the automorphism group of \(Z_2^6\).

MSC:

05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
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References:

[1] Godsil, Algebraic Graph Theory (2001) · doi:10.1007/978-1-4613-0163-9
[2] DOI: 10.1007/BF02579389 · Zbl 0648.05031 · doi:10.1007/BF02579389
[3] DOI: 10.1007/BF02582929 · Zbl 0587.05046 · doi:10.1007/BF02582929
[4] DOI: 10.1016/S0012-365X(01)00438-1 · Zbl 1018.05044 · doi:10.1016/S0012-365X(01)00438-1
[5] DOI: 10.1007/BF02582961 · Zbl 0663.05043 · doi:10.1007/BF02582961
[6] DOI: 10.1016/0012-365X(92)90711-N · Zbl 0771.05048 · doi:10.1016/0012-365X(92)90711-N
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