On Certain Properties of the P-Unitary Cayley Graph over a Finite Ring

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