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Complexity
Volume 2018, Article ID 5745628, 10 pages
https://doi.org/10.1155/2018/5745628
Research Article

The Strong Local Diagnosability of a Hypercube Network with Missing Edges

Min Xie,1,2 Jiarong Liang,2,3 and Xi Xiong2,3

1School of Automation Science and Engineering, South China University of Technology, 510640, China
2School of Computer and Electronics Information, Guangxi University, 530004, China
3School of Computer and Electronics Information, Guangxi Key Laboratory of Multimedia Communications and Network Technology, 530004, China

Correspondence should be addressed to Jiarong Liang; moc.361@25760177931

Received 15 April 2018; Revised 5 July 2018; Accepted 13 August 2018; Published 4 October 2018

Academic Editor: Michele Scarpiniti

Copyright © 2018 Min Xie et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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 dimensions, denoted by , the SLD of a node is equal to its degree when . 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 . 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 -dimensions is greater than , then the SLD of any node is still equal to its RD provided that the number of faulty edges does not exceed . If the RD of each node is greater than , then the SLD of each node is also equal to its RD, no matter how many faulty edges exist in .