78,624 research outputs found

    Super edge-connectivity and matching preclusion of data center networks

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    Edge-connectivity is a classic measure for reliability of a network in the presence of edge failures. kk-restricted edge-connectivity is one of the refined indicators for fault tolerance of large networks. Matching preclusion and conditional matching preclusion are two important measures for the robustness of networks in edge fault scenario. In this paper, we show that the DCell network Dk,nD_{k,n} is super-λ\lambda for k2k\geq2 and n2n\geq2, super-λ2\lambda_2 for k3k\geq3 and n2n\geq2, or k=2k=2 and n=2n=2, and super-λ3\lambda_3 for k4k\geq4 and n3n\geq3. Moreover, as an application of kk-restricted edge-connectivity, we study the matching preclusion number and conditional matching preclusion number, and characterize the corresponding optimal solutions of Dk,nD_{k,n}. In particular, we have shown that D1,nD_{1,n} is isomorphic to the (n,k)(n,k)-star graph Sn+1,2S_{n+1,2} for n2n\geq2.Comment: 20 pages, 1 figur

    Further topics in connectivity

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    Continuing the study of connectivity, initiated in §4.1 of the Handbook, we survey here some (sufficient) conditions under which a graph or digraph has a given connectivity or edge-connectivity. First, we describe results concerning maximal (vertex- or edge-) connectivity. Next, we deal with conditions for having (usually lower) bounds for the connectivity parameters. Finally, some other general connectivity measures, such as one instance of the so-called “conditional connectivity,” are considered. For unexplained terminology concerning connectivity, see §4.1.Peer ReviewedPostprint (published version

    Synthetic reverberating activity patterns embedded in networks of cortical neurons

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    Synthetic reverberating activity patterns are experimentally generated by stimulation of a subset of neurons embedded in a spontaneously active network of cortical cells in-vitro. The neurons are artificially connected by means of conditional stimulation matrix, forming a synthetic local circuit with a predefined programmable connectivity and time-delays. Possible uses of this experimental design are demonstrated, analyzing the sensitivity of these deterministic activity patterns to transmission delays and to the nature of ongoing network dynamics.Comment: 8 pages, 5 figure
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