Minimum dominating sets

Minimum dominating sets (MDSet) of protein interaction networks allow the control of underlying protein interaction networks through their topological placement. While essential proteins are enriched in MDSets, we hypothesize that the statistical properties of biological functions of essential genes are enhanced when we focus on essential MDSet proteins (e-MDSet).

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Recently, several studies have drawn attention to the determination of a minimum set of driver proteins that are important for the control of the underlying protein-protein interaction (PPI) networks. In general, the minimum dominating set (MDS) model is widely adopted.

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Several recent studies have used the Minimum Dominating Set (MDS) model to identify driver nodes, which provide the control of the underlying networks, in protein interaction networks. There may exist multiple MDS configurations in a given network, thus it is difficult to determine which one represents the real set of driver nodes.

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The minimum number of colors needed for a dominated coloring of G is called the dominated chromatic number of G, denoted by χdom (G). In this paper, dominated coloring of graphs is compared with (open) packing number of G and it is shown that if G is a graph of order n with diam(G) ≥ 3, then χdom(G) ≤ n − ρ(G) and if ρ0(G) = 2n/3, then χdom(G) = ρ0(G).

9p nutifooddau 21-01-2019 18 1   Download

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí toán học quốc tế đề tài: Minimum connected dominating sets of random cubic graphs...

13p thulanh4 11-09-2011 50 1   Download