Graph theoretic reliability analysis for the Boolean \(n\) cube networks. (English) Zbl 0656.94027

Yang, C. S.; Wang, J. F.; Lee, J. Y.; Boesch, F. T.

IEEE Trans. Circuits Syst. 35, No. 9, 1175-1179 (1988).

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 \(\lambda\) (see Definition 3) for the Boolean \(n\)-cube network is equal to \(2^ n\).

MSC:

94C15

Applications of graph theory to circuits and networks

Keywords:

maximum line connectivity; network reliability of the Boolean \(n\)-cube network; spanning trees; super line-connectivity