Domination Reliability. Dohmen, K. & Tittmann, P. Electron. J. Combin., 19:#P15, 2012. 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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