{2,3}-Restricted connectivity of locally twisted cubes
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TLDR
The n-dimensional locally twisted cubes, denoted by LTQ n, are a well-known network topology for building multiprocessor systems and the h-restricted connectivity is shown to be the minimum cardinality of a set of nodes in G whose deletion disconnects G.About:
This article is published in Theoretical Computer Science.The article was published on 2016-02-15 and is currently open access. It has received 38 citations till now. The article focuses on the topics: Connectivity.read more
Citations
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Proceedings Article
The Conditional Node Connectivity of the k-ary n-Cube.
TL;DR: In this article, the authors derived the conditional node connectivity of the k-ary n-cube interconnection network under the condition of forbidden faulty sets (i.e., assuming that each non-faulty processor has at least one non-Faulty neighbor).
Journal ArticleDOI
The generalized 4-connectivity of hypercubes
Shangwei Lin,Qianhua Zhang +1 more
TL;DR: It is shown that the generalized 4-connectivity of the n -dimensional hypercube Q n is ( n − 1 ) , that is, for any four vertices in Q n, there exist internally disjoint trees connecting them inQ n.
On Restricted Connectivity and Extra Connectivity of Hypercubes and Folded Hypercubes
TL;DR: For the hypercube Qn and the folded hypercube FQn, it was shown in this article that κ1(Qn) =κ(1)(Qn)=2n-2 for n≥3, κ2(Qns) =3n-5 for n ≥ 4, and κ 1(FQn), κ 2(Fqs) =4n-4 for n ≤ 8.
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Structure connectivity and substructure connectivity of bubble-sort star graph networks
Guozhen Zhang,Dajin Wang +1 more
TL;DR: The problem of structure/substructure connectivity in bubble-sort star networks is studied and it is proved that for P 2 k + 1, a path on odd nodes is proved and for a cycle on 2k nodes C2k, there are only cycles on even nodes in BSn.
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h -restricted connectivity of locally twisted cubes
Chia-Chen Wei,Sun-Yuan Hsieh +1 more
TL;DR: This paper examines a generalized h -restricted connectivity measure for n -dimensional locally twisted cube and reveals that ź h ( L T Q n ) = 2 h ( n - h ) for 0 Ż h ź n - 2 .
References
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Book
Introduction to Graph Theory
TL;DR: In this article, the authors introduce the concept of graph coloring and propose a graph coloring algorithm based on the Eulers formula for k-chromatic graphs, which can be seen as a special case of the graph coloring problem.
Book
Topological Structure and Analysis of Interconnection Networks
TL;DR: This book provides the most basic problems, concepts, and well-established results from the topological structure and analysis of interconnection networks in the graph-theoretic language for undergraduates and postgraduates specializing in computer science and applied mathematics.
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Generalized measures of fault tolerance with application to N-cube networks
TL;DR: The author presents a fault-tolerance analysis for the n-cube networks that shows that such networks can tolerate up to 2n-3 processor failures and remain connected provided that for each processor p in the network, all the processors which are directly connected to p do not fail at the same time.
Journal ArticleDOI
On the extraconnectivity of graphs
J. Fàbrega,Miguel Angel Fiol +1 more
TL;DR: Substantial conditions are given, relating the diameter of G with its girth, to assure optimum values of these conditional connectivities of G.
Journal ArticleDOI
Conditional connectivity measures for large multiprocessor systems
TL;DR: The vertex connectivity for the n-dimensional cube is obtained, and the minimal sets of faulty nodes that disconnect the cube are characterized.