Combinatorial properties of a rooted graph polynomial

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Combinatorial properties of a rooted graph polynomial

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dc.contributor.author Eisenstat, D.
dc.contributor.author Gordon, Gary
dc.contributor.author Redlich, A.
dc.date.accessioned 2012-02-16T20:47:43Z
dc.date.available 2012-02-16T20:47:43Z
dc.date.issued 2008
dc.identifier.citation Eisenstat, D., et al. (2008). "Combinatorial properties of a rooted graph polynomial." SIAM Journal on Discrete Mathematics 22 (2): 776-785. en_US
dc.identifier.uri http://hdl.handle.net/10385/900
dc.description.abstract 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) = ... = EV(k-1)(G; 1) = 0. We find bounds on the first and second derivatives of EV (G; p); applications yield characterizations of rooted paths and cycles in terms of the polynomial. We prove reconstruction results for rooted trees and a negative result concerning reconstruction of more complicated rooted graphs. We also prove that the norm of the largest root of EV(G; p) in Q[i] gives a sharp lower bound on the number of vertices of G. en_US
dc.publisher SIAM Journal on Discrete Mathematics en_US
dc.title Combinatorial properties of a rooted graph polynomial en_US
dc.type Article en_US
dc.identifier.doi 10.1137/06065951X

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