A Normal Non-Cayley-Invariant Graph for the Elementary Abelian Group of Order 64

Abstract

We exhibit an interesting Cayley graph X of the elementary abelian group Z6 2 with the property that Aut(X) contains two regular subgroups, exactly one of which is normal. This demonstrates the existence of two subsets of Z6 2 that yield isomorphic Cayley graphs, even though the two subsets are not equivalent under the automorphism group of Z6 2 . 2000 Mathematics subject classification: 05C25.

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