Geodesic
Domination reliability
The electronic journal of combinatorics, Tome 19 (2012) no. 1
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In this paper, 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 formulæ 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.
DOI : 10.37236/1166
Classification : 05C69, 05C65, 68M15, 05C31, 90B15
Mots-clés : reliability, domination, decomposition, inclusion-exclusion, broken circuit, cograph, hypergraph, NP-hard 
@article{10_37236_1166,
     author = {Klaus Dohmen and Peter Tittmann},
     title = {Domination reliability},
     journal = {The electronic journal of combinatorics},
     year = {2012},
     volume = {19},
     number = {1},
     doi = {10.37236/1166},
     zbl = {1243.05183},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1166/}
}
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Klaus Dohmen; Peter Tittmann. Domination reliability. The electronic journal of combinatorics, Tome 19 (2012) no. 1. doi: 10.37236/1166

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