  In recent work, we study certain Cayley graphs associated with a finite
commutative ring and their multiplicative subgroups. Among various results that
we prove, we provide the necessary and sufficient conditions for such a Cayley
graph to be prime. In this paper, we continue this line of research.
Specifically, we investigate some basic properties of certain $p$-unitary
Cayeley graphs associated with a finite commutative ring. In particular, under
some mild conditions, we provide the necessary and sufficient conditions for
this graph to be prime.
