1. Reliability Analysis of (n , k)-Bubble-Sort Networks Based on Extra Conditional Fault.
- Author
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Zhao, Lina, Wang, Shiying, and Dou, Feng
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- *
INTEGERS - Abstract
Given a graph G = (V (G) , V (E)) , a non-negative integer g and a set of faulty vertices F ⊆ V (G) , the g-extra connectivity of G, denoted by κ g (G) , is the smallest cardinality of F, whose value of deletion, if exists, will disconnect G and give each remaining component at least g + 1 vertices. The g-extra diagnosability of the graph G, denoted by t g (G) , is the maximum cardinality of the set F of fault vertices that the graph can guarantee to identify under the condition that each fault-free component has more than g vertices. In this paper, we determine that g-extra connectivity of (n , k) -bubble-sort network B n , k is κ g (B n , k) = n + g (k − 2) − 1 for 4 ≤ k ≤ n − 1 and 0 ≤ g ≤ n − k . Afterwards, we show that g-extra diagnosability of B n , k under the PMC model (4 ≤ k ≤ n − 1 and 0 ≤ g ≤ n − k) and MM* model (4 ≤ k ≤ n − 1 and 0 ≤ g ≤ min { n − k − 1 , k − 2 }) is t g (B n , k) = n + g (k − 1) − 1 , respectively. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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