Royle, Gordon F. A normal non-Cayley-invariant graph for the elementary abelian group of order 64. (English) Zbl 1167.05035 J. Aust. Math. Soc. 85, No. 3, 347-351 (2008). 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 \(Z_2^6\). Cited in 6 Documents MSC: 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) Keywords:Cayley graph; CI-graph; strongly regular graph PDFBibTeX XMLCite \textit{G. F. Royle}, J. Aust. Math. Soc. 85, No. 3, 347--351 (2008; Zbl 1167.05035) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.