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On the roots of strongly connected reliability polynomials
Author(s) -
Brown J. I.,
Dilcher K.
Publication year - 2009
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.20301
Subject(s) - digraph , strongly connected component , mathematics , reliability (semiconductor) , vertex connectivity , combinatorics , simply connected space , unit disk , plane (geometry) , arc (geometry) , closure (psychology) , complex plane , connected component , discrete mathematics , vertex (graph theory) , graph , mathematical analysis , geometry , physics , power (physics) , quantum mechanics , economics , market economy
The 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