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

Hao, Rong‐Xia; Tian, Zeng-Xian; Xu, Jie

doi:10.1016/j.tcs.2016.02.024

Cited by 47 publications

(3 citation statements)

References 40 publications

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“…Given a graph G and a nonnegative integer h, the h-extra connectivity of G, denoted by κ (h) (G), is the cardinality of a minimum vertex-cut S of G, if it exists, such that each component of G−S has at least h+1 vertices. In fact, the extra connectivity plays an important indicator of a network's ability for diagnosis and fault tolerance [22,26,30,31]. Currently, the known results of h-extra connectivity for alternating group graphs and split-stars were proposed in [31] and [30], respectively.…”

Section: Discussionmentioning

confidence: 99%

The Component Connectivity of Alternating Group Graphs and Split-Stars

Gu,

Hao,

Chang

2018

Preprint

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For an integer 2, the -component connectivity of a graph G, denoted by κ (G), is the minimum number of vertices whose removal from G results in a disconnected graph with at least components or a graph with fewer than vertices. This is a natural generalization of the classical connectivity of graphs defined in term of the minimum vertex-cut and is a good measure of robustness for the graph corresponding to a network. So far, the exact values of -connectivity are known only for a few classes of networks and small 's. It has been pointed out in [Component connectivity of the hypercubes, Int. J. Comput. Math. 89 (2012) 137-145] that determining -connectivity is still unsolved for most interconnection networks, such as alternating group graphs and star graphs. In this paper, by exploring the combinatorial properties and fault-tolerance of the alternating group graphs AG n and a variation of the star graphs called split-stars S 2 n , we study their -component connectivities. We obtain the following results: (i) κ 3 (AG n ) = 4n−10 and κ 4 (AG n ) = 6n−16 for n 4, and κ 5 (AG n ) = 8n − 24 for n 5; (ii) κ 3 (S 2 n ) = 4n − 8, κ 4 (S 2 n ) = 6n − 14, and κ 5 (S 2 n ) = 8n − 20 for n 4.

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Section: Discussionmentioning

confidence: 99%

The Component Connectivity of Alternating Group Graphs and Split-Stars

Gu,

Hao,

Chang

2018

Preprint

Self Cite

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“…Given a graph G and a nonnegative integer h, the h-extra connectivity of G, denoted by κ (h) (G), is the cardinality of a minimum vertex-cut S of G, if it exists, such that each component of G − S has at least h + 1 vertices. In fact, the extra connectivity plays an important indicator of a network's ability for diagnosis and fault tolerance [25], [31], [35], [36]. Currently, the known results of h-extra connectivity for alternating group graphs and splitstars were proposed in [36] and [35], respectively.…”

Section: B Split-stars and Their Propertiesmentioning

confidence: 99%

Measuring the Vulnerability of Alternating Group Graphs and Split-Star Networks in Terms of Component Connectivity

Hao

Chang

2019

IEEE Access

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For an integer 2, the -component connectivity of a graph G, denoted by κ (G), is the minimum number of vertices whose removal from G results in a disconnected graph with at least components or a graph with fewer than vertices. This is a natural generalization of the classical connectivity of graphs defined in term of the minimum vertex-cut and a good measure of vulnerability for the graph corresponding to a network. So far, the exact values of -connectivity are known only for a few classes of networks and small 's. It has been pointed out in component connectivity of the hypercubes, International Journal of Computer Mathematics 89 (2012) 137-145] that determining -connectivity is still unsolved for most interconnection networks such as alternating group graphs and star graphs. In this paper, by exploring the combinatorial properties and the fault-tolerance of the alternating group graphs AG n and a variation of the star graphs called split-stars S 2 n , we study their -component connectivities. We obtain the following results: 1) κ 3 (AG n ) = 4n − 10 and κ 4 (AG n ) = 6n − 16 for n 4, and κ 5 (AG n ) = 8n − 24 for n 5 and 2) κ 3 (S 2 n ) = 4n − 8, κ 4 (S 2 n ) = 6n − 14, and κ 5 (S 2 n ) = 8n − 20 for n 4.

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“…How to sustain the performance and dependability of large-scale multiprocessor systems has been brought to the fore in the existence of processor failures. Thus, fault diagnosis is the most essential step in constructing and maintaining multiprocessor systems [1,2,3]. Using a topological structure of the interconnection network, a multiprocessor system can be taken as an undirected graph which consists of many nodes acting as processors and many edges acting as communication links.…”

Section: Introductionmentioning

confidence: 99%

The Component Diagnosability of General Networks

Zhuang,

Guo,

et al. 2021

Preprint

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The processor failures in a multiprocessor system have a negative impact on its distributed computing efficiency. Because of the rapid expansion of multiprocessor systems, the importance of fault diagnosis is becoming increasingly prominent. The h-component diagnosability of G, denoted by ct h (G), is the maximum number of nodes of the faulty set F that is correctly identified in a system, and the number of components in G − F is at least h. In this paper, we determine the (h + 1)component diagnosability of general networks under the PMC model and MM * model. As applications, the component diagnosability is explored for some well-known networks, including complete cubic networks, hierarchical cubic networks, generalized exchanged hypercubes, dual-cube-like networks, hierarchical hypercubes, Cayley graphs generated by transposition trees (except star graphs), and DQcube as well. Furthermore, we provide some compare results between the component diagnosability and other fault diagnosabilities.

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

Cited by 47 publications

References 40 publications

The Component Connectivity of Alternating Group Graphs and Split-Stars

The Component Connectivity of Alternating Group Graphs and Split-Stars

Measuring the Vulnerability of Alternating Group Graphs and Split-Star Networks in Terms of Component Connectivity

The Component Diagnosability of General Networks

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