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Domination Reliability (1103.3854v1)
Published 20 Mar 2011 in math.CO, cs.DM, and math.PR
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.
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