TY - JOUR
A2 - Cruz, Frederico R. B.
AU - Zhang, Ke
AU - Zhao, Haixing
AU - Ye, Zhonglin
AU - Dong, Lixin
PY - 2018
DA - 2018/10/14
TI - A Recursive Formula for the Reliability of a -Uniform Complete Hypergraph and Its Applications
SP - 3131087
VL - 2018
AB - 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.
SN - 1024-123X
UR - https://doi.org/10.1155/2018/3131087
DO - 10.1155/2018/3131087
JF - Mathematical Problems in Engineering
PB - Hindawi
KW -
ER -