26 research outputs found

    Edge-Fault Tolerance of Hypercube-like Networks

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    This paper considers a kind of generalized measure λs(h)\lambda_s^{(h)} of fault tolerance in a hypercube-like graph GnG_n which contain several well-known interconnection networks such as hypercubes, varietal hypercubes, twisted cubes, crossed cubes and M\"obius cubes, and proves λs(h)(Gn)=2h(n−h)\lambda_s^{(h)}(G_n)= 2^h(n-h) for any hh with 0⩽h⩽n−10\leqslant h\leqslant n-1 by the induction on nn and a new technique. This result shows that at least 2h(n−h)2^h(n-h) edges of GnG_n have to be removed to get a disconnected graph that contains no vertices of degree less than hh. Compared with previous results, this result enhances fault-tolerant ability of the above-mentioned networks theoretically

    Cyclic sums, network sharing and restricted edge cuts in graphs with long cycles

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    Cyclic Sums, Network Sharing and Restricted Edge Cuts in Graphs with Long Cycles Dieter Rautenbach , Lutz Volkmann Preprint series: 07-06, 8 MSC 2000 05A17 Partitions of integers 05C40 Connectivity Abstract We study graphs G = (V,E) containing a long cycle which for given integers a1, a2, ..., ak 2 N have an edge cut whose removal results in k components with vertex sets V1, V2, ..., Vk such that |Vi| ai for 1 i k. Our results closely relate to problems and recent research in network sharing and network reliability. Keywords: restricted edge connectivity, arbitrarily vertex decomposable graph, network reliability, network sharin
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