Zero Divisor Graphs of Upper Triangular Matrix Rings.

Let R be a commutative ring with identity 1 ≠ 0 and T be the ring of all n × n upper triangular matrices over R. In this paper, we describe the zero divisor graphof T. Some basic graph theory properties ofare given, including determination of the girth and diameter. The structure ofis 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 ofis fully described and an explicit formula for the number of edges is given. [ABSTRACT FROM PUBLISHER]