September 21, 2017: Jim Coykendall

Recently there has been much activity in the intersection of commutative algebra and graph theory. In particular, there has been much attention to the so called “zero-divisor graph” and a number of its natural variants. The idea behind the zero-divisor graph is to take as vertices the nonzero zero-divisors of a commutative ring with identity and declare that there is an edge between $x,y\in R$ if and only if $xy = 0$. There are a number of striking properties that this graph possesses, probably the most interesting of which is that this graph is connected and has diameter no more than 3.