Leavitt path algebras of Cayley graphs arising from cyclic groups

For any positive integer $n$ we describe the Leavitt path algebra of the Cayley graph $C_n$ corresponding to the cyclic group $\Z/n\Z$. Using a Kirchberg-Phillips-type realization result, we show that there are exactly four isomorphism classes of such Leavitt path algebras, arising as the algebras corresponding to the graphs $C_i$ ($3\leq i \leq 6$).