RAIRO-Theor. Inf. Appl.
Volume 53, Number 3-4, July–December 2019
|Page(s)||85 - 113|
|Published online||24 October 2019|
Edge-bipancyclicity in conditional edge-faulty k-ary n-cubes*
School of Mathematics and Computer Science, Shanxi Normal University,
Shanxi 041004, PR China
2 School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, PR China.
** Corresponding author: email@example.com
Accepted: 3 July 2019
The class of k-ary n-cubes represents the most commonly used interconnection topology for parallel and distributed computing systems. In this paper, we consider the faulty k-ary n-cube with even k ≥ 4 and n ≥ 2 such that each vertex of the k-ary n-cube is incident with at least two healthy edges. Based on this requirement, we investigate the fault-tolerant capabilities of the k-ary n-cube with respect to the edge-bipancyclicity. We prove that in the k-ary n-cube Qnk, every healthy edge is contained in fault-free cycles of even lengths from 6 to |V(Qnk)|, even if the Qnk has up to 4n − 5 edge faults and our result is optimal with respect to the number of edge faults tolerated.
Mathematics Subject Classification: 05C38
Key words: Interconnection network / fault-tolerant / k-ary n-cube / conditional edge-fault / edge-bipancyclicity
© EDP Sciences, 2020
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