The Extra Connectivity and Conditional Diagnosability of Alternating Group Networks

Lin, Limei; Zhou, Shuming; Xu, Li; Wang, Dajin

doi:10.1109/tpds.2014.2347961

Cited by 90 publications

(28 citation statements)

References 44 publications

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“…Application to the alternating group graphs AG n Remark 1. It is known that κ 1 (AG n ) = 4n − 11 for n ≥ 5 determined by Lin et al [33] and t p (AG n ) = 4n − 11 obtained by Tsai [37]. As a corollary of Theorem 1, we immediately obtain the following result which contains the above result.…”

Section: 1supporting

confidence: 65%

“…As applications, the pessimistic diagnosability for each of split-star networks S 2 n , Cayley graphs generated by transposition trees Γ n , Cayley graph generated by the 2-tree Γ n (∆) and the burnt pancake networks BP n is gotten. As corollaries, the known results about the extra connectivity and the pessimistic diagnosability of many famous networks including the alternating group graphs [33], [37], the alternating group networks [45] , BC networks [47], [19] and the k-ary n-cube networks [15], [13], [30], [41] are obtained directly.…”

Section: Discussionmentioning

confidence: 99%

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Equal relation between the extra connectivity and pessimistic diagnosability for some regular graphs

Hao

et al. 2017

Theoretical Computer Science

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Extra connectivity and the pessimistic diagnosis are two crucial subjects for a multiprocessor system's ability to tolerate and diagnose faulty processor. The pessimistic diagnosis strategy is a classic strategy based on the PMC model in which isolates all faulty vertices within a set containing at most one fault-free vertex. In this paper, the result that the pessimistic diagnosability t p (G) equals the extra connectivity κ 1 (G) of a regular graph G under some conditions are shown. Furthermore, the following new results are gotten: the pessimistic diagnosability t p (S 2 n ) = 4n − 9 for split-star networks S 2 n ; t p (Γ n ) = 2n − 4 for Cayley graphs generated by transposition trees Γ n ; t p (Γ n (∆)) = 4n−11 for Cayley graph generated by the 2-tree Γ n (∆); t p (BP n ) = 2n−2 for the burnt pancake networks BP n . As corollaries, the known results about the extra connectivity and the pessimistic diagnosability of many famous networks including the alternating group graphs; the alternating group networks; BC networks; the k-ary n-cube networks etc. are obtained directly.

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Section: 1supporting

confidence: 65%

Section: Discussionmentioning

confidence: 99%

Equal relation between the extra connectivity and pessimistic diagnosability for some regular graphs

Hao

et al. 2017

Theoretical Computer Science

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“…They consider the situation that any fault set cannot contain all the neighbor vertices of any vertex in a system. The restricted diagnosability of the system has received much attention [5,6,20,24,25,38]. In 2012, Peng et al [27] proposed a measure for fault diagnosis of the system, namely, the g-good-neighbor diagnosability (which is also called the ggood-neighbor conditional diagnosability), which requires that every fault-free node has at least g fault-free neighbors.…”

Section: Introductionmentioning

confidence: 99%

The 2-good-neighbor connectivity and 2-good-neighbor diagnosability of bubble-sort star graph networks

Wang

2017

Discrete Applied Mathematics

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Connectivity plays an important role in measuring the fault tolerance of interconnection networks. The g-good-neighbor connectivity of an interconnection network G is the minimum cardinality of g-good-neighbor cuts. Diagnosability of a multiprocessor system is one important study topic. A new measure for fault diagnosis of the system restrains that every fault-free node has at least g fault-free neighbor vertices, which is called the g-good-neighbor diagnosability of the system. As a famous topology structure of interconnection networks, the n-dimensional bubblesort star graph BS n has many good properties. In this paper, we prove that 2-good-neighbor connectivity of BS n is 8n − 22 for n ≥ 5 and the 2-good-neighbor connectivity of BS 4 is 8; the 2-good-neighbor diagnosability of BS n is 8n − 19 under the PMC model and MM * model for n ≥ 5.

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“…Motivated by the research on the extra connectivity of some networks, including hypercubes, BC networks, hypercube-like networks, alternating group graphs, and split-star networks [2], [4], [21], [25], [31], [32], [40], we establish the g-extra connectivity for the (n, k)-arrangement graph A n,k , and show that the A n,k 's one-extra connectivity is…”

Section: Introductionmentioning

confidence: 99%

The Extra Connectivity, Extra Conditional Diagnosability, and <inline-formula> <tex-math notation="LaTeX"> $t/m$</tex-math> </inline-formula>-Diagnosability of Arrangement Graphs

Zhou

Hsieh

2016

IEEE Trans. Rel.

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Extra connectivity is an important indicator of the robustness of a multiprocessor system in presence of failing processors. The g-extra conditional diagnosability and the t/mdiagnosability are two important diagnostic strategies at systemlevel that can significantly enhance the system's self-diagnosing capability. The g-extra conditional diagnosability is defined under the assumption that every component of the system removing a set of faulty vertices has more than g vertices. The t/mdiagnosis strategy can detect up to t faulty processors which might include at most m misdiagnosed processors, where m is typically a small integer number. In this paper, we analyze the combinatorial properties and fault tolerant ability for an (n, k)-arrangement graph, denoted by A n,k , a well-known interconnection network proposed for multiprocessor systems. We first establish that the A n,k 's one-extra connectivity is (2k − 1) 3 (k ≥ 4, n ≥ k + 2), and three-extra connectivity is (4k − 4)(n − k) − 4 ( k ≥ 4, n ≥ k + 2 or k ≥ 3, n ≥ k + 3), respectively. And then, we address the g-extra conditional diagnosability of A n,k under the PMC model for 1 ≤ g ≤ 3. Finally, we determine that the (n, k)-arrangement graph A n,k is [(2k − 1)(n − k) − 1]/1-diagnosable (k ≥ 4, n ≥ k + 2), [(3k − 2)(n − k) − 3]/2-diagnosable (k ≥ 4, n ≥ k + 2), and [(4k − 4)(n − k) − 4]/3-diagnosable (k ≥ 4, n ≥ k + 3) under the PMC model, respectively.

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The Extra Connectivity and Conditional Diagnosability of Alternating Group Networks

Cited by 90 publications

References 44 publications

Equal relation between the extra connectivity and pessimistic diagnosability for some regular graphs

Equal relation between the extra connectivity and pessimistic diagnosability for some regular graphs

The 2-good-neighbor connectivity and 2-good-neighbor diagnosability of bubble-sort star graph networks

The Extra Connectivity, Extra Conditional Diagnosability, and <inline-formula> <tex-math notation="LaTeX"> $t/m$</tex-math> </inline-formula>-Diagnosability of Arrangement Graphs

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