Conditional connectivity measures for large multiprocessor systems

Latifi, Shahram; Hegde, Maruti; Naraghi-Pour, Mort

doi:10.1109/12.262126

Cited by 286 publications

(84 citation statements)

References 7 publications

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“…For κ h , Esfahanian [3] determined κ 1 (Q n ) = 2n − 2, and this was further generalized by Latifi et al [8] …”

Section: κ(G) ≤ λ(G) ≤ δ(G) Where δ(G) Is the Minimum Degree Of G Amentioning

confidence: 99%

Super Connectivity of Line Graphs and Digraphs

Lü

2006

Acta Mathematicae Applicatae Sinica, English Series

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The h-super connectivity κ h and the h-super edge-connectivity λ h are more refined network reliability indices than the connectivity and the edge-connectivity. This paper shows that for a connected balanced digraph D and its line digraph L, if D is optimally super edge-connected, then κ 1 (L) = 2λ 1 (D), and that for a connected graph G and its line graph L, if one of κ 1 (L) and λ 2 (G) exists, then κ 1 (L) = λ 2 (G). This paper determines that κ 1 (B(d, n)) is equal to 4d − 8 for n = 2 and d ≥ 4, and to 4d − 4 for n ≥ 3 and d ≥ 3, and that κ 1 (K(d, n)) is equal to 4d − 4 for d ≥ 2 and n ≥ 2 except K(2, 2). It then follows that B(d, n) and K(d, n) are both super connected for any d ≥ 2 and n ≥ 1.

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“…For κ h , Esfahanian [3] determined κ 1 (Q n ) = 2n − 2, and this was further generalized by Latifi et al [8] …”

Section: κ(G) ≤ λ(G) ≤ δ(G) Where δ(G) Is the Minimum Degree Of G Amentioning

confidence: 99%

Super Connectivity of Line Graphs and Digraphs

Lü

2006

Acta Mathematicae Applicatae Sinica, English Series

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“…To overcome such a shortcoming, Harary [2] introduced the concept of conditional connectivity by appending some requirements on connected components, Latifi et al [3] specified requirements and proposed the concept of the restricted h-connectivity. These parameters can measure fault tolerance of an interconnection network more accurately than the classical connectivity.…”

Section: Introductionmentioning

confidence: 99%

Embedded connectivity of recursive networks

Dong

Yan

et al. 2016

Theoretical Computer Science

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Let G n be an n-dimensional recursive network. The h-embedded connectivity ζ h (G n ) (resp. edge-connectivity η h (G n )) of G n is the minimum number of vertices (resp. edges) whose removal results in disconnected and each vertex is contained in an h-dimensional subnetwork G h . This paper determines ζ h and η h for the hypercube Q n and the star graph S n , and η 3 for the bubble-sort network B n .

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“…Because the connectivity has some shortcomings, Esfahanian [1] proposed the concept of restricted connectivity, Latifi et al [3] generalized it to restricted h-connectivity which can measure fault tolerance of an interconnection network more accurately than the classical connectivity. The concepts stated here are slightly different from theirs.…”

Section: Introductionmentioning

confidence: 99%

Generalized measures of fault tolerance in exchanged hypercubes

2013

Information Processing Letters

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The exchanged hypercube EH(s, t), proposed by Loh et al. [The exchanged hypercube, IEEE Transactions on Parallel and Distributed Systems 16 (9) (2005) 866-874], is obtained by removing edges from a hypercube Q s+t+1 . This paper considers a kind of generalized measures κ (h) and λ (h) of fault tolerance in EH(s, t) with 1 s t and determines κ (h) (EH(s, t)) = λ (h) (EH(s, t)) = 2 h (s + 1 − h) for any h with 0 h s. The results show that at least 2 h (s + 1 − h) vertices (resp. 2 h (s + 1 − h) edges) of EH(s, t) have to be removed to get a disconnected graph that contains no vertices of degree less than h, and generalizes some known results.

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Conditional connectivity measures for large multiprocessor systems

Cited by 286 publications

References 7 publications

Super Connectivity of Line Graphs and Digraphs

Super Connectivity of Line Graphs and Digraphs

Embedded connectivity of recursive networks

Generalized measures of fault tolerance in exchanged hypercubes

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