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Nature Research, Scientific Reports, 1(3), 2013

DOI: 10.1038/srep01736

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Minimum Dominating Sets in Scale-Free Network Ensembles

Journal article published in 2013 by F. Molnár ORCID, S. Sreenivasan, B. K. Szymanski, G. Korniss
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

We study the scaling behavior of the size of minimum dominating set (MDS) in scale-free networks, with respect to network size N and power-law exponent γ, while keeping the average degree fixed. We study ensembles generated by three different network construction methods, and we use a greedy algorithm to approximate the MDS. With a structural cutoff imposed on the maximal degree we find linear scaling of the MDS size with respect to N in all three network classes. Without any cutoff (kmax = N - 1) two of the network classes display a transition at γ ≈ 1.9, with linear scaling above, and vanishingly weak dependence below, but in the third network class we find linear scaling irrespective of γ. We find that the partial MDS, which dominates a given z < 1 fraction of nodes, displays essentially the same scaling behavior as the MDS.