Graph Theoretic Reliability Analysis for the Boolean N Cube Networks

It is well known that there are several papers which deal with the Boolean n-cube network and applications. However, no theoretical work has been done in calculating the network reliability of the Boolean n-cube network. In this paper, two graph theoretic results concerning about the problem of the 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 (see Definition 6) property. Thus the number of line disconnecting sets (a set of lines whose removal results in a disconnected or trivial graph) of order λ (see Definition 3) for the Boolean n-cube network is equal to 2n.