It is known (and can easily be seen) that a unitary cayley graph on $n=\prod_ip_i$, ($p_i$ prime) vertices with $n$ squarefree can be recognized as the tensor product of the graphs $K_{p_i}$, where $K_n$ denotes the complete graph on $n$ vertices. 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?

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

It is known (and can easily be seen) that a unitary cayley graph on $n=\prod_ip_i,\ (p_i\ \text{prime})$ vertices with $n$ squarefree can be recognized as the tensor product of the graphs $K_{p_i}$, where $K_n$ denotes the complete graph on $n$ vertices. 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?

It is known (and can easily be seen) that a unitary cayley graph on $n=\prod_ip_i$, ($p_i$ prime) vertices with $n$ squarefree can be recognized as the tensor product of the graphs $K_{p_i}$, where $K_n$ denotes the complete graph on $n$ vertices. 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?

It is known (and can easily be seen) that a unitary cayley graph on $n=\prod_ip_i,\ (p_i\ \text{prime})$ 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?

It is known (and can easily be seen) that a unitary cayley graph on $n=\prod_ip_i,\ (p_i\ \text{prime})$ vertices with $n$ squarefree can be recognized as the tensor product of the graphs $K_{p_i}$, where $K_n$ denotes the complete graph on $n$ vertices. 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?