Domination Reliability. Dohmen, K. & Tittmann, P. Electron. J. Combin., 19:#P15, 2012.
Domination Reliability [link]Paper  abstract   bibtex   
We propose a new network reliability measure for some particular kind of service networks, which we refer to as domination reliability. We relate this new reliability measure to the domination polynomial of a graph and the coverage probability of a hypergraph. We derive explicit and recursive formulae for domination reliability and its associated domination reliability polynomial, deduce an analogue of Whitney's broken circuit theorem, and prove that computing domination reliability is NP-hard.
@article{ Dohmen:2012:DR,
  author = {Klaus Dohmen and Peter Tittmann},
  title = {Domination Reliability},
  journal = {Electron. J. Combin.},
  year = {2012},
  volume = {19},
  pages = {#P15},
  url = {http://www.combinatorics.org/ojs/index.php/eljc/article/view/v19i1p15},
  abstract = {We propose a new network reliability measure for some
                  particular kind of service networks, which we refer to
                  as domination reliability. We relate this new
                  reliability measure to the domination polynomial of a
                  graph and the coverage probability of a hypergraph. We
                  derive explicit and recursive formulae for domination
                  reliability and its associated domination reliability
                  polynomial, deduce an analogue of Whitney's broken
                  circuit theorem, and prove that computing domination
                  reliability is NP-hard.},
  keywords = {graph, domination, reliability, polynomial, NP-hard,
                  inclusion-exclusion, broken circuit}
}

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