Conditional Fault Diagnosability of Dual-Cubes

Zhou, Shuming; Chen, Lanxiang; Xu, Jie

doi:10.1142/s0129054112500256

Cited by 20 publications

(6 citation statements)

References 38 publications

(54 reference statements)

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“…The graph S is the dual-cube DC p . (Note that DC p was observed to be a Cayley graph of the semidirect product Q G in [42]; however, the definition of DC p as such on [42, p. 1734] is incorrect.) Consider the following more complex construction.…”

Section: Some Examplesmentioning

confidence: 99%

Using semidirect products of groups to build classes of interconnection networks

Stewart

2020

Discrete Applied Mathematics

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Section: Some Examplesmentioning

confidence: 99%

Using semidirect products of groups to build classes of interconnection networks

Stewart

2020

Discrete Applied Mathematics

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“…A dual-cube DC n is an (n + 1)regular bipartite graph of order 2 2n+1 . Moreover, Zhou et al [49] showed that DC n is a Cayley graph, and so DC n is vertex-transitive. Since DC n is an (n + 1)-regular bipartite graph, and so it contains no C 3 , according to Lemma 3.21, if P 3 = (x, y, z) is a 3-path, where xz / ∈ E(G), then |N(x) ∩ N(y)| = |N(y) ∩ N(z)| = 0 and |N(x) ∩ N(z)| 2, and so the number of neighbors of P 3 in DC n can be counted as follows.…”

Section: K-ary N-cube Networkmentioning

confidence: 99%

“…Zhou et al [49] determined κ 2 (DC n ) = 3n − 2 and t c (DC n ) = 3n − 2 for n ≥ 3, dependently. By Theorem 2.4, we immediately obtain the following result which contains the above results.…”

Section: K-ary N-cube Networkmentioning

confidence: 99%

Relationship between conditional diagnosability and 2-extra connectivity of symmetric graphs

Hao

Tian

2016

Theoretical Computer Science

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The conditional diagnosability and the 2-extra connectivity are two important parameters to measure ability of diagnosing faulty processors and faulttolerance in a multiprocessor system. The conditional diagnosability t c (G) of G is the maximum number t for which G is conditionally t-diagnosable under the comparison model, while the 2-extra connectivity κ 2 (G) of a graph G is the minimum number k for which there is a vertex-cut F with |F | = k such that every component of G − F has at least 3 vertices. A quite natural problem is what is the relationship between the maximum and the minimum problem? This paper partially answer this problem by proving t c (G) = κ 2 (G) for a regular graph G with some acceptable conditions. As applications, the conditional diagnosability and the 2-extra connectivity are determined for some well-known classes of vertex-It is well known that a topological structure of an interconnection network N can be modeled by a graph G = (V, E), where V represents the set of components such as processors and E represents the set of communication links in N (see a text-book by Xu [42]). Faults of some processors and/or communication lines in a large-scale system are inevitable. People are concerned with how to diagnose faults and to determine fault tolerance of the system.

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“…The semidirect product of groups is also used to prove that some networks are Cayley graphs. For example, using the semidirect product, Zhou et al [39] showed that the dual-cube DC n is a Cayley graph…”

Section: Replacement Product Of Cayley Graphsmentioning

confidence: 99%

On restricted edge-connectivity of replacement product graphs

Hong

2016

Sci. China Math.

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This paper considers the edge-connectivity and the restricted edge-connectivity of replacement product graphs, gives some bounds on edge-connectivity and restricted edge-connectivity of replacement product graphs and determines the exact values for some special graphs. In particular, the authors further confirm that under certain conditions, the replacement product of two Cayley graphs is also a Cayley graph, and give a necessary and sufficient condition for such Cayley graphs to have maximum restricted edge-connectivity. Based on these results, the authors construct a Cayley graph with degree d whose restricted edge-connectivity is equal to d + s for given odd integer d and integer s with d 5 and 1 s d − 3, which answers a problem proposed ten years ago.

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Conditional Fault Diagnosability of Dual-Cubes

Cited by 20 publications

References 38 publications

Using semidirect products of groups to build classes of interconnection networks

Using semidirect products of groups to build classes of interconnection networks

Relationship between conditional diagnosability and 2-extra connectivity of symmetric graphs

On restricted edge-connectivity of replacement product graphs

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