Let R be a commutative ring with non-zero identity. For a natural number n we associate a simple graph denoted by ‎ T^nR with R^n-{0} as the vertex set and two distinct verticesX and Y in R^n are adjacent if and only if there exists‎ an nxn lover triangular matrix over R whose entries on the main diagonal are non-zero such that AX^T=Y^T or‎ AY^T=X^T. When we consider the ring R with multiplication as a semigroup, the T^1R is the usual undirected cayley graph. In this note we study some basic properties of T^nR.

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