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Article . 2009 . Peer-reviewed
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Article . 2009
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Article . 2009
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On the roots of strongly connected reliability polynomials

Authors: Jason I. Brown; Karl Dilcher;

On the roots of strongly connected reliability polynomials

Abstract

AbstractThe strongly connected reliability scRel(D, p) of a digraph D is the probability that the spanning subgraph of D consisting of the operational arcs is strongly connected, given that the vertices always operate, but each arc independently operates with probability p ∈ [0, 1]. We provide here some results on the location of the roots of strongly connected reliability polynomials that contrast sharply with what is known for all terminal reliability. We show that not only there can be negative real roots, but also roots of arbitrarily large modulus. In fact, the closure of the roots of strongly connected reliability polynomials contains all of the complex plane except, possibly, some subset of the unit disk centered at z = 1. © 2009 Wiley Periodicals, Inc. NETWORKS, 2009

Related Organizations
Keywords

roots, Connectivity, reliability, Colbourn conjecture, Brown, digraph, Graph polynomials, Reliability, availability, maintenance, inspection in operations research, all terminal reliability, strongly connected

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
4
Average
Average
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