Graphically abelian groups |
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Authors: | Richard Goldstone |
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Institution: | Department of Mathematics and Computer Science, Manhattan College, Riverdale, NY 10471, United States |
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Abstract: | We define a group G to be graphically abelian if the function g?g−1 induces an automorphism of every Cayley graph of G. We give equivalent characterizations of graphically abelian groups, note features of the adjacency matrices for Cayley graphs of graphically abelian groups, and show that a non-abelian group G is graphically abelian if and only if G=E×Q, where E is an elementary abelian 2-group and Q is a quaternion group. |
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Keywords: | Cayley graph Quasi-abelian Cayley graph Normal Cayley graph Hamiltonian group |
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