Abstract
Let Γ and Δ be finite groups. We give a sufficient condition to prove that every Cayley graph of Γ is isomorphic to a Cayley graph of Δ . As an application of this result, it is proved that every Cayley graph of a certain group of order 12 is isomorphic to a Cayley graph of the dihedral group of order 12. Analogously, it is proved that every Cayley graph of a cyclic group of order 2 k is isomorphic to a Cayley graph of the dihedral group D k , and the converse holds if and only if k ∈ { 2 , 3 , 5 } . For Cayley digraphs it is proved that every Cayley digraph of Z 2 k , generated with H ⊆ { 2 α } α = 1 k - 1 , is isomorphic to a Cayley digraph in D k .
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