Conditional Diagnosability of Alternating Group Graphs

  • Authors:
  • Rong-Xia Hao;Yan-Quan Feng;Jin-Xin Zhou

  • Affiliations:
  • Beijing Jiaotong University, Beijing;Beijing Jiaotong Univerity, Beijing;Beijing Jiaotong Univerity, Beijing

  • Venue:
  • IEEE Transactions on Computers
  • Year:
  • 2013

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Abstract

Let $(A_n)$ be the alternating group of degree $(n)$ with $(n\ge 3)$. Set $(S=\{(1 2 i), (1 i 2) \vert3\le i\le n\})$. The alternating group graph, denoted by $(AG_n)$, is defined as the Cayley graph on $(A_n)$ with respect to $(S)$. Jwo et al. [Networks 23 (1993) 315-326] introduced alternating group graph $(AG_n)$ as an interconnection network topology for computing systems. Conditional diagnosability, a new measure of diagnosability introduced by Lai et al. [IEEE Transactions on Computers 54(2) (2005) 165-175] can better measure the diagnosability of regular interconnection networks. This paper determines that under PMC-model the conditional diagnosability of $(AG_n)$ is 4 for $(n=4)$ and $(6n-18)$ for each $(n\ge 5)$.