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On the nonexistence of uniformly optimal graphs for pair‐connected reliability
Author(s) -
Amin A. T.,
Siegrist K. T.,
Slater P. J.
Publication year - 1991
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.3230210307
Subject(s) - combinatorics , mathematics , vertex connectivity , vertex (graph theory) , probabilistic logic , enhanced data rates for gsm evolution , reliability (semiconductor) , discrete mathematics , graph , connectivity , computer science , statistics , physics , telecommunications , power (physics) , quantum mechanics
We consider probabilistic graphs G = (V, E) in which each edge xy ∈ E fails independently with probability q . The reliability measure studied is pair‐connectivity, the expected number of pairs of connected vertices. We examine how the coefficients of the pair‐connected reliability polynomial are determined by the subgraph structure of G , and we use these results to show that in most cases there does not exist a uniformly optimal n ‐vertex, m ‐edge graph.