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

机译：γ均匀完全超图的可靠性递推公式及其应用

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摘要

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 (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.
机译：有限图或超图S =（V，E）的可靠性多项式R（S，p）给出了S的操作边或超边分别诱发连接的跨子图或子超图的可能性，并假设所有（超）边S的概率以相同的概率q = 1-p独立失败。在本文中，我们研究了具有随机失效的超边的超图的超边诱发连接的跨子超图的可能性。 （超）图的可靠性计算是一个NP难题。我们为具有超边故障的r均匀完整超图的可靠性提供递归关系。因此，我们确定并计算r-均匀完整超图中具有给定大小的连通跨子超图的数量。

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  • 来源
    《Mathematical Problems in Engineering》 |2018年第13期|3131087.1-3131087.7|共7页
  • 作者

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

  • 作者单位

    Qinghai Normal Univ Sch Comp Xining 810008 Qinghai Peoples R China|Key Lab Tibetan Informat Proc & Machine Translat Xining 810008 Qinghai Peoples R China|Minist Educ Key Lab Tibetan Informat Proc Xining 810008 Qinghai Peoples R China;

    Qinghai Normal Univ Sch Comp Xining 810008 Qinghai Peoples R China|Key Lab Tibetan Informat Proc & Machine Translat Xining 810008 Qinghai Peoples R China|Minist Educ Key Lab Tibetan Informat Proc Xining 810008 Qinghai Peoples R China|Shaanxi Normal Univ Sch Comp Sci Xian 710062 Shaanxi Peoples R China;

    Key Lab Tibetan Informat Proc & Machine Translat Xining 810008 Qinghai Peoples R China|Minist Educ Key Lab Tibetan Informat Proc Xining 810008 Qinghai Peoples R China|Shaanxi Normal Univ Sch Comp Sci Xian 710062 Shaanxi Peoples R China;

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