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

Ke Zhang, Haixing Zhao, Zhonglin Ye and Lixin Dong

Mathematical Problems in Engineering, 2018, vol. 2018, 1-7

Abstract:

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.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:3131087

DOI: 10.1155/2018/3131087

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