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A theorem concerning cyclic directed graphs with applications to network reliability
Author(s) -
Willie Randall R.
Publication year - 1980
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.3230100107
Subject(s) - reliability (semiconductor) , terminal (telecommunication) , directed acyclic graph , directed graph , combinatorics , mathematics , computer science , discrete mathematics , topology (electrical circuits) , computer network , power (physics) , physics , quantum mechanics
In a recent paper, Satyanarayana and Prabhakar have presented a new topological formula for evaluating exact reliability of terminal‐pair directed networks. Terms in the formula are associated in a one‐to‐one fashion with certain acyclic subgraphs of the network, cyclic subgraphs being of no importance. In their paper, however, the proof that cyclic subgraphs may be ignored seems to be incomplete. We consider an alternate proof of this fact.