Title: Zero Divisor Graphs
Abstract: We give an overview of the research on zero divisor graphs, including the three main definitions, beginning with the original definition introduced by I. Beck in 1988. In addition, we discuss in detail zero divisor graphs determined by equivalence classes of annihilator ideals. We discuss connectivity, completeness, diameter, and girth, as well as other graph theoretic properties, and what this information can reveal about the ring. This is joint work with Jim Coykendall and Sean Sather-Wagstaff at North Dakota State University and Laura Sheppardson at the University of Mississippi. This talk is suitable for beginning graduate students.