Unitary Cayley graphs whose Roman domination numbers are at most four

Abstract

Let R be a finite commutative ring with nonzero identity. The unitary Cayley graph of R is the graph obtained by letting all the elements of R to be the vertices and defining distinct vertices x and y to be adjacent if and only if x – y is a unit element of R. In this paper, we characterize all unitary Cayley graphs with Roman domination number at most four.