A Recursive Formula for the Reliability of a r-Uniform Complete Hypergraph and Its Applications

Ke Zhang, Haixing Zhao, Zhonglin Ye, Lixin Dong
2018 Mathematical Problems in Engineering  
The reliability polynomial R(S,p) of a finite graph or hypergraph S=(V,E) gives the probability that the operational edges or hyperedges of S induce a connected spanning subgraph or subhypergraph, respectively, assuming that all (hyper)edges of S fail independently with an identical probability q=1-p. In this paper, we investigate the probability that the hyperedges of a hypergraph with randomly failing hyperedges induce a connected spanning subhypergraph. The computation of the reliability for
more » ... (hyper)graphs is an NP-hard problem. We provide recurrence relations for the reliability of r-uniform complete hypergraphs with hyperedge failure. Consequently, we determine and calculate the number of connected spanning subhypergraphs with given size in the r-uniform complete hypergraphs.
doi:10.1155/2018/3131087 fatcat:azmaf2lyubg4vdnnevwodhbug4