ComputingComputer EngineeringComputer ScienceComputer NetworksFault-tolerant ComputingFault-tolerant SystemsGraph AlgorithmsGraph TheoryNetwork ConnectivityNetwork ReliabilityNetwork TheoryNetwork TopologyGraph-theoretic Network AnalysisN-cube NetworksNode ConnectivityReliability BoundsReliability FunctionSuper Connectivity
Two graph-theoretic results concerning Boolean n-cube network reliability are presented. First, a simple formula for the number of spanning trees of the Boolean n-cube network is derived. As a result, the reliability function for large failure rate can be readily computed. Second, the Boolean n-cube network is proved to have the super-line-connectivity property. Thus the number of line-disconnecting sets (a set of lines the removal of which results in a disconnected or trivial graph) or order lambda for the Boolean n-cube network is equal to 2/sup n/.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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