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Abstract
A characterization is given of the class of edge-transitive Cayley graphs of Frobenius groups $\mathbb{Z}_{p^{d}}{:}\mathbb{Z}_{q}$ with p,q odd prime, of valency coprime to p. This characterization is then used to study an isomorphism problem regarding Cayley graphs, and to construct new families of half-arc-transitive graphs.
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