The Disconnection Number of a Graph
Dr. Matt Cropper / Eastern Kentucky University
The disconnection number of a (topological) graph G, D(G), is the smallest positive integer such that the removal of any D(G) points (not necessarily vertices) from G disconnects the graph. A cut-point in a graph is a point (not necessarily a vertex) whose removal disconnects the graph. This talk will concern the size of the set of graphs with a finite set of non-cut points and the size of the set of graphs with a given disconnection number.