A Recursive Formula for the Reliability of a r -Uniform Complete Hypergraph and Its Applications
Joint Authors
Zhang, Ke
Ye, Zhonglin
Dong, Lixin
Zhao, Haixing
Source
Mathematical Problems in Engineering
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-10-14
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Zhang, Ke& Zhao, Haixing& Ye, Zhonglin& Dong, Lixin. 2018. A Recursive Formula for the Reliability of a r -Uniform Complete Hypergraph and Its Applications. Mathematical Problems in Engineering،Vol. 2018, no. 2018, pp.1-7.
https://search.emarefa.net/detail/BIM-1206687
Modern Language Association (MLA)
Zhang, Ke…[et al.]. A Recursive Formula for the Reliability of a r -Uniform Complete Hypergraph and Its Applications. Mathematical Problems in Engineering No. 2018 (2018), pp.1-7.
https://search.emarefa.net/detail/BIM-1206687
American Medical Association (AMA)
Zhang, Ke& Zhao, Haixing& Ye, Zhonglin& Dong, Lixin. A Recursive Formula for the Reliability of a r -Uniform Complete Hypergraph and Its Applications. Mathematical Problems in Engineering. 2018. Vol. 2018, no. 2018, pp.1-7.
https://search.emarefa.net/detail/BIM-1206687
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1206687