Abstract
A characterization is given of the class of edge-transitive Cayley graphs of Frobenius groups Zrd:Zm with r an odd prime and m odd, of valency less than 2p1 with p1 the smallest prime divisor of m. It is shown that either (rd,m)=(p,p−12)or(29,7), or such a graph is a normal Cayley graph and half-transitive. This provides new construction of half-transitive graphs.
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