Abstract: Monomial ideals associated with (unweighted, unoriented) graphs have been studied extensively since the introduction of edge ideals by Villarreal in 1990. More recently, motivated by applications in coding theory, interest has arisen in a generalization of edge ideals to weighted, oriented graphs. In this talk I will review basic definitions and what is known about the regularity of the edge ideals of unweighted, unoriented graphs before discussing the regularity of edge ideals of weighted, oriented paths and cycles.
