Automorphism groups of some generalized Cayley graphs

Let R be a commutative ring with identity element. Graph Gamma(n)(R) is defined with vertex set R-n\{0} and two distinct vertices X and Y are adjacent if and only if there exists an nxn lower triangular matrix A with non-zero diagonal entries such that AX(T) = Y-T or AY(T) = X-T. By B-T, we mean transpose of matrix B. If R is a semigroup with respect to multiplication and n = 1, then Gamma(1)(R) is the undirected Cayley graph. In this paper, a prime number p, we find the clique number and automorphism group of Gamma(n)(R), where R = Z(p2) or R = Z(p3).