On the spanning <i>w</i>‐wide diameter of the star graph

Lin, Cheng-Kuan; Huang, Hua-Min; Hsu, David; Hsu, Lih‐Hsing

doi:10.1002/net.20135

Cited by 11 publications

(3 citation statements)

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“…Assume that G is k * -connected.We may also define the k * -connected distance between any two vertices u and v, denoted by d There are some studies on the k * -diameter of some interconnection networks [4], [20]. Later, we will study D s n (B n ) and D s 2 (B n ).…”

Section: Resultsmentioning

confidence: 99%

The Spanning Connectivity of the Burnt Pancake Graphs

Chin

Weng

Hsu

et al. 2009

IEICE Trans. Inf. & Syst.

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Section: Resultsmentioning

confidence: 99%

The Spanning Connectivity of the Burnt Pancake Graphs

Chin

Weng

Hsu

et al. 2009

IEICE Trans. Inf. & Syst.

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“…In many recent papers involving the wide diameter, the focus has been on finding or bounding the wide diameter of particular classes of graphs. See (13,21,22) for examples. Several other measures of recent interest such as the Rabin number, the fault tolerant diameter, and the edge wide diameter also share a strong relation to the concept of property P d , m as they bring together the ideas of diameter and containers between vertices in an attempt to measure the reliability of networks.…”

Section: Introductionmentioning

confidence: 99%

Property P_d,m and efficient design of reliable networks

2012

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“…The diameter and fault diameters of star graphs were computed in [1,22,34]. Some other interesting properties of star graphs are studied in [12,14,[25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Conditional Diagnosability of Cayley Graphs Generated by Transposition Trees Under the Comparison Diagnosis Model

et al. 2008

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The diagnosis of faulty processors plays an important role in multiprocessor systems for reliable computing, and the diagnosability of many well-known networks has been explored. Zheng et al. showed that the diagnosability of *This work was supported in part by the National Science Council of the Republic of China under Contract NSC 95-2221-E-009-134-MY3. 83 J. Inter. Net. 2008.09:83-97. Downloaded from www.worldscientific.com by UNIVERSITY OF QUEENSLAND on 08/16/15. For personal use only. 84 C.-K. Lin et al. the n-dimensional star graph S n is n -1. Lai et al. introduced a restricted diagnosability of multiprocessor systems called conditional diagnosability. They consider the situation when no faulty set can contain all the neighbors of any vertex in the system. In this paper, we study the conditional diagnosability of Cayley graphs generated by transposition trees (which include the star graphs)under the comparison model, and show that it is 3n -8 for n > 4, except for the n-dimensional star graph, for which it is 3n -7. Hence the conditional diagnosability of these graphs is about three times larger than their classical diagnosability.

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On the spanning w‐wide diameter of the star graph

Cited by 11 publications

References 21 publications

The Spanning Connectivity of the Burnt Pancake Graphs

The Spanning Connectivity of the Burnt Pancake Graphs

Property P_d,m and efficient design of reliable networks

Conditional Diagnosability of Cayley Graphs Generated by Transposition Trees Under the Comparison Diagnosis Model

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On the spanning w‐wide diameter of the star graph

Cited by 11 publications

References 21 publications

The Spanning Connectivity of the Burnt Pancake Graphs

The Spanning Connectivity of the Burnt Pancake Graphs

Property Pd,m and efficient design of reliable networks

Conditional Diagnosability of Cayley Graphs Generated by Transposition Trees Under the Comparison Diagnosis Model

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Product

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Property P_d,m and efficient design of reliable networks