Title:  An algebraic study of Cameron-Walker graphs

Abstract:  Given a finite simple graph G, two commonly studied invariants in graph theory are the matching number, m(G), and the induced matching number of a graph, i(G). These combinatorial invariants provide upper and lower bounds, respectively, for the (Castelnuovo-Mumford) regularity of the quotient of the edge ideal associated to the graph, R/I(G). Cameron and Walker characterize all graphs where the matching number is the same as the induced matching number and therefore the regularity can be explicitly calculated. In this talk we will examine other algebraic and combinatorial properties of R/I(G) where G satisfies m(G)=i(G), such as Cohen-Macaulayness, shellability, and vertex decomposability.