Restricted connectivity and restricted fault
                    diameter of some interconnection networks

Li, Qiao; Zhang, Yi

doi:10.1090/dimacs/021/18

Cited by 7 publications

(4 citation statements)

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“…With the assumption that each node was incident with at least one fault-free node, the connectivities of hypercubes [9], k-ary n-cubes [6], cube-connected cycles [20], undirected de Bruijn networks [20], and Kautz networks [20] were computed. Moreover, the fault diameters of hypercubes [18] and star graphs [21] were obtained.…”

Section: Discussionmentioning

confidence: 99%

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Embedding fault-free cycles in crossed cubes with conditional link faults

Hung

Chen

2008

J Supercomput

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The crossed cube, which is a variation of the hypercube, possesses some properties that are superior to those of the hypercube. In this paper, we show that with the assumption of each node incident with at least two fault-free links, an ndimensional crossed cube with up to 2n − 5 link faults can embed, with dilation one, fault-free cycles of lengths ranging from 4 to 2 n . The assumption is meaningful, for its occurrence probability is very close to 1, and the result is optimal with respect to the number of link faults tolerated. Consequently, it is very probable that algorithms executable on rings of lengths ranging from 4 to 2 n can be applied to an n-dimensional crossed cube with up to 2n − 5 link faults.

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Section: Discussionmentioning

confidence: 99%

“…On the other hand, with an assumption that each node is incident with at least one fault-free node, connectivities and fault diameters were computed on some networks [9,20]. With another assumption that each node is incident with at least two faultfree links, Hamiltonian properties were investigated on some networks [3,4,12,15,23].…”

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confidence: 99%

Embedding fault-free cycles in crossed cubes with conditional link faults

Hung

Chen

2008

J Supercomput

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“…[11] ( [7]), and the R 1 -node-connectivities of cube-connected cycles, undirected binary de Bruijn networks and Kautz graphs are all greater by one at most than their node-connectivities [23]. Besides, the maximal diameters of an n-cube with 2n − 3 node faults and an n-dimensional star network with 2n − 5 node faults are n + 2 [19] and 3(n − 1)/2 + 2 [29], respectively.…”

Section: Introductionmentioning

confidence: 99%

Fault-free longest paths in star networks with conditional link faults

Tsai

Chen

2009

Theoretical Computer Science

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“…On the other hand, Harary introduced in [16] the concept of conditional faults. Let P represent a property of a graph G and S be a vertex subset of G. The P-connectivity of G was defined to be the minimum |S| so that G À S is disconnected and every component of G À S satisfies the property P. Considering P the property that each node is incident with at least one fault-free node, P-connectivities were computed for hypercubes [9], k-ary n-cubes [5], cubes-connected cycles [23], undirected de Bruijn networks [23], and Kautz networks [23]. In addition, under the same assumption (i.e., the property P), the diameters of hypercubes and star graphs were computed in [21,24], respectively.…”

Section: Introductionmentioning

confidence: 99%