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

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  • Ke Zhang
  • Haixing Zhao
  • Zhonglin Ye
  • Lixin Dong

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.

Suggested Citation

  • Ke Zhang & Haixing Zhao & Zhonglin Ye & Lixin Dong, 2018. "A Recursive Formula for the Reliability of a -Uniform Complete Hypergraph and Its Applications," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-7, October.
  • Handle: RePEc:hin:jnlmpe:3131087
    DOI: 10.1155/2018/3131087
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