2,206 research outputs found

    Edge-Fault Tolerance of Hypercube-like Networks

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    This paper considers a kind of generalized measure Ξ»s(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 Ξ»s(h)(Gn)=2h(nβˆ’h)\lambda_s^{(h)}(G_n)= 2^h(n-h) for any hh with 0β©½hβ©½nβˆ’10\leqslant h\leqslant n-1 by the induction on nn and a new technique. This result shows that at least 2h(nβˆ’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

    On Linkedness of Cartesian Product of Graphs

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    We study linkedness of Cartesian product of graphs and prove that the product of an aa-linked and a bb-linked graphs is (a+bβˆ’1)(a+b-1)-linked if the graphs are sufficiently large. Further bounds in terms of connectivity are shown. We determine linkedness of product of paths and product of cycles
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