Domination in Generalized Cayley Graph of Commutative Rings

Let R be a commutative ring with identity and n be a natural number. The generalized Cayley graph of R, denoted by Gamma(n)(R), is the graph whose vertex set is R-n\{0} and two distinct vertices X and Y are adjacent if and only if there exists an nxn lower triangular matrix A over R whose entries on the main diagonal are non-zero such that AX(T) = Y-T or AY(T) = X-T, where for a matrix B, B-T is the matrix transpose of B. In this paper, we give some basic properties of Gamma(n)(R) and we determine the domination parameters of Gamma(n)(R).