ZERO DIVISOR GRAPHS OF UPPER TRIANGULAR MATRIX RINGS
Let R be a commutative ring with identity 1 not equal 0 and T be the ring of all n x n upper triangular matrices over R. In this paper, we describe the zero divisor graph (Gamma) over right arrow (T) of T. Some basic graph theory properties of (Gamma) over right arrow (T) are given, including determination of the girth and diameter. The structure of (Gamma) over right arrow (T) is discussed, and bounds for the number of edges are given. In the case that R is a finite integral domain and n = 2, the structure of (Gamma) over right arrow (T) is fully described and an explicit formula for the number of edges is given.
upper triangular matrix ring commutative ring zero-divisor graph