On the fault-tolerant diameter and wide diameter of ω-connected graphs

  • Authors:

  • Jian-Hua Yin;Jiong-Sheng Li;Guo-Liang Chen;Cheng Zhong

  • Affiliations:

  • Department of Applied Mathematics, College of Information Science and Technology, Hainan University, Haikou, Hainan 570228, People's Republic of China;Department of Mathematics, University of Science and Technology of China, Hefei 230026, People's Republic of China;Department of Computer Science, University of Science and Technology of China, Hefei 230027, People's Republic of China;Department of Computer Science, University of Science and Technology of China, Hefei 230027, People's Republic of China

  • Venue:
  • Networks
  • Year:
  • 2005

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Abstract

The fault-tolerant diameter, Dk, and wide diameter, dk, are two important parameters for measuring the reliability and efficiency of interconnection networks. It is well known that for any ω-connected graph G and any integer k, 1 ≤ k ≤ ω, we have Dk ≤ dk. However, what we are interested in is how large the difference between dk and Dk can be. For any 2-connected graph G with diameter d, Flandrin and Li proved that d2 ≤ D2 + 1 if d = 2 and d2 ≤ (d - 1)(D2 - 1) if d ≥ 3. In this article, we further prove that d2 ≤ max{D2 + 1, (d - 1)(D2 - d) + 2} for d ≤ ⌈(D2 - 1)/2⌉ and d2 ≤ max{D2 + 1,⌊(D2 - 1)2/4⌋ + 2} for d ≥ ⌈(D2 - 1)/2⌉ + 1, and we also show that this upper bound can be achieved. Moreover, for any ω(≥ 3)-connected graph G, we prove that dω ≤ Dω + 1 if Dω - 1 = 2 and dω ≤ max{Dω + 2,⌊(Dω)2/4⌋ + 2} if Dω - 1 = 2 and Dω - 1 ≥ 3. © 2005 Wiley Periodicals, Inc. NETWORKS, Vol. 45(2), 88–94 2005