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The Disconnection Number of a Graph

Dr. Matt Cropper

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.

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