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The Strong Local Diagnosability of a Hypercube Network with Missing Edges

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  • Min Xie
  • Jiarong Liang
  • Xi Xiong

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 .

Suggested Citation

  • Min Xie & Jiarong Liang & Xi Xiong, 2018. "The Strong Local Diagnosability of a Hypercube Network with Missing Edges," Complexity, Hindawi, vol. 2018, pages 1-10, October.
    • Handle: RePEc:hin:complx:5745628
    DOI: 10.1155/2018/5745628
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