Combinatorial Properties of a Rooted Graph Polynomial

For a rooted graph G, let EV (G; p) be the expected number of vertices reachable from the root when each edge has an independent probability p of operating successfully. We examine combinatorial properties of this polynomial, proving that G is k-edge connected if and only if EV (G; 1) =

• Type: Journal
• Year: 2008
• Where: SIAMDM
• Authors: David Eisenstat, Gary Gordon, Amanda Redlich
• Keywords: Expected Number, Independent Probability, Rooted Graphs, SIAMDM 2008