It is known (and can easily be seen) that a unitary cayley graph on $n=\prod_ip_i$ vertices with $n$ squarefree can be recognized as the tensor product of the graphs $K_{p_i}$. Is a similar characterization possible for all other unitary cayley graphs i.e., when $n$ is not squarefree? Further is such a characterization possible for all perfect cayley graphs?