A theorem concerning cyclic directed graphs with applications to network reliability

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Abstract
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.

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