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

摘要

The reliability polynomial of a finite graph or hypergraph gives the probability that the operational edges or hyperedges of induce a connected spanning subgraph or subhypergraph, respectively, assuming that all (hyper)edges of fail independently with an identical probability . 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 (hyper)graphs is an NP-hard problem. We provide recurrence relations for the reliability of -uniform complete hypergraphs with hyperedge failure. Consequently, we determine and calculate the number of connected spanning subhypergraphs with given size in the -uniform complete hypergraphs.