The Strong Local Diagnosability of a Hypercube Network with Missing Edges
Joint Authors
Xie, Min
Liang, Jiarong
Xiong, Xi
Source
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-10-04
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
In the research on the reliability of a connection network, diagnosability is an important problem that should be considered.
In this article, a new concept regarding diagnosability, called strong local diagnosability (SLD), which describes the local status of the strong diagnosability (SD) of a system, is presented.
In addition, a few important results related to the SLD of a node of a system are presented.
Based on these results, we conclude that in a hypercube network of n dimensions, denoted by Qn, the SLD of a node is equal to its degree when n⩾4.
Moreover, we explore the SLD of a node of an incomplete hypercube network.
We determine that the SLD of a node is equal to its remaining degree (RD) in an incomplete hypercube network, which is true provided that the number of faulty edges in this hypercube network does not exceed n−3.
Finally, we discuss the SLD of a node for an incomplete hypercube network and obtain the following results: if the minimum RD of nodes in an incomplete hypercube network of n-dimensions is greater than 3, then the SLD of any node is still equal to its RD provided that the number of faulty edges does not exceed 7n−3−1.
If the RD of each node is greater than 4, then the SLD of each node is also equal to its RD, no matter how many faulty edges exist in Qn.
American Psychological Association (APA)
Xie, Min& Liang, Jiarong& Xiong, Xi. 2018. The Strong Local Diagnosability of a Hypercube Network with Missing Edges. Complexity،Vol. 2018, no. 2018, pp.1-10.
https://search.emarefa.net/detail/BIM-1134782
Modern Language Association (MLA)
Xie, Min…[et al.]. The Strong Local Diagnosability of a Hypercube Network with Missing Edges. Complexity No. 2018 (2018), pp.1-10.
https://search.emarefa.net/detail/BIM-1134782
American Medical Association (AMA)
Xie, Min& Liang, Jiarong& Xiong, Xi. The Strong Local Diagnosability of a Hypercube Network with Missing Edges. Complexity. 2018. Vol. 2018, no. 2018, pp.1-10.
https://search.emarefa.net/detail/BIM-1134782
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1134782