### Abstract

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.

Original language | English |
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Pages (from-to) | 1175-1179 |

Number of pages | 5 |

Journal | IEEE Transactions on Circuits and Systems |

Volume | 35 |

Issue number | 9 |

DOIs | |

Publication status | Published - 1988 Jan 1 |

### All Science Journal Classification (ASJC) codes

- Engineering(all)

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## Cite this

*IEEE Transactions on Circuits and Systems*,

*35*(9), 1175-1179. https://doi.org/10.1109/31.7582