Paper Info
Title
Reliability of DQcube Based on g-Extra Conditional Fault
Abstract
Diagnosability and connectivity are important metrics for the reliability and fault diagnosis capability of interconnection networks, respectively. The g-extra connectivity of a graph G, denoted by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\kappa _g(G)$</tex> , is the minimum number of vertices whose deletion will disconnect the network and every remaining component has more than <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$g$</tex> vertices. The g-extra conditional diagnosability of graph G, denoted by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$t_g(G)$</tex> , is the maximum number of faulty vertices that the graph G can guarantee to identify under the condition that every fault-free component contains at least g+1 vertices. In this paper, we first determine that g-extra connectivity of DQcube is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\kappa _g(G)=(g+1)(n+1)-\frac{g(g+3)}{2}$</tex> for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$0\leq g\leq n-3$</tex> and then show that the g-extra conditional diagnosability of DQcube under the PMC model <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(n\geq 4, 1\leq g\leq n-3)$</tex> and the MM <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$^\ast$</tex> model <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(n\geq 7, 1\leq g\leq \frac{n-3}{4})$</tex> is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$t_g(G)=(g+1)(n+1)-\frac{g(g+3)}{2}+g$</tex> , respectively.
Year
DOI
Venue
2021
10.1093/comjnl/bxaa058
The Computer Journal
Keywords
DocType
Volume
g-extra connectivity,g-extra conditional diagnosability,MM* model,PMC model
Journal
64
Issue
ISSN
Citations 
9
0010-4620
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Hong Zhang1719126.06
Jixiang Meng235355.62