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Title

SOME NORMAL EDGE-TRANSITIVE CAYLEY GRAPHS ON QUATERNION GROUPS

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Abstract

 LET G BE A GROUP AND LET S BE A SUBSET OF G SUCH THAT 1GÏS AND S=S−1. LET G=CAY(G, S) BE A CAYLEY GRAPH ON G RELATIVE TO S. THEN G IS SAID TO BE NORMAL EDGE-TRANSITIVE, IF NAUT(G)(G) ACTS TRANSITIVELY ON EDGES. IN THIS PAPER WE DETERMINE ALL NORMAL EDGE-TRANSITIVE CAYLEY GRAPHS ON A QUATERNION GROUP Q2N OF VALENCY 4. IN ADDITION WE GIVE NORMAL EDGE-TRANSITIVE CAYLEY GRAPHS ON A QUATERNION GROUP Q2N OF SOME OTHER VALENCIES.

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