(untitled) (Journal of Mathematical Study, 2021)
Let R be a commutative ring with identity and n be a natural number. The generalized Cayley graph of R, denoted by Γ^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 n×n 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 Γ^n_R and we determine the domination parameters of Γ^n_R.