Edge-fault-tolerant bipancyclicity of Cayley graphs generated by transposition-generating trees

2014 ◽  
Vol 92 (7) ◽  
pp. 1345-1352 ◽  
Author(s):  
Weihua Yang ◽  
Hengzhe Li ◽  
Wei-hua He
Keyword(s):  
Fault Tolerant ◽  
Cayley Graphs ◽  
Generating Trees

The Relationship Between Extra Connectivity and t/k-Diagnosability of Regular Networks

2020 ◽  
Vol 20 (01) ◽  
pp. 2050003
Author(s):  
WENJUN LIU
Keyword(s):  
Fault Tolerant ◽  
Cayley Graphs ◽  
General Relationship ◽  
Multiprocessor System ◽  
Diagnostic Model ◽  
Star Network ◽  
Minimum Number ◽  
Two Parameters ◽  
Regular Networks ◽  
The Relationship

The g-extra connectivity of a multiprocessor system modeled by a graph G, denoted by [Formula: see text] (G), is the minimum number of removed vertices such that the network is disconnected and each residual component has no less than g + 1 vertices. The t/k-diagnosis strategy can detect up to t faulty processors which might include at most k misdiagnosed processors. These two parameters are important to measure the fault tolerant ability of a multiprocessor system. The extra connectivity and t/k-diagnosability of many well-known networks have been investigated extensively and independently. However, the general relationship between the extra connectivity and the t/k-diagnosability of general regular networks has not been established. In this paper, we explore the relationship between the k-extra connectivity and t/k-diagnosability for regular networks under the classic PMC diagnostic model. More specifically, we derive the relationship between 1-extra connectivity and pessimistic diagnosability for regular networks. Furthermore, the t/k-diagnosability and pessimistic diagnosability of some networks, including star network, BC networks, Cayley graphs generated by transposition trees etc., are determined.

FAULT-TOLERANT MAXIMAL LOCAL-CONNECTIVITY ON CAYLEY GRAPHS GENERATED BY TRANSPOSITION TREES

2009 ◽  
Vol 10 (03) ◽  
pp. 253-260 ◽  
Author(s):  
LUN-MIN SHIH ◽  
CHIEH-FENG CHIANG ◽  
LIH-HSING HSU ◽  
JIMMY J. M. TAN
Keyword(s):  
Cayley Graph ◽  
Fault Tolerant ◽  
Minimum Degree ◽  
Cayley Graphs ◽  
Disjoint Paths ◽  
Local Connectivity ◽  
Vertex Disjoint

The local connectivity of two vertices is defined as the maximum number of internally vertex-disjoint paths between them. In this paper, we define two vertices as maximally local-connected, if the maximum number of internally vertex-disjoint paths between them equals the minimum degree of these two vertices. Moreover, we show that an (n-1)-regular Cayley graph generated by transposition tree is maximally local-connected, even if there are at most (n-3) faulty vertices in it, and prove that it is also (n-1)-fault-tolerant one-to-many maximally local-connected.

Fault-Tolerant Maximal Local-Connectivity on Cayley Graphs Generated by Transpositions

2019 ◽  
Vol 30 (08) ◽  
pp. 1301-1315 ◽  
Author(s):  
Liqiong Xu ◽  
Shuming Zhou ◽  
Weihua Yang
Keyword(s):  
Fault Tolerance ◽  
Interconnection Networks ◽  
Fault Tolerant ◽  
Interconnection Network ◽  
Cayley Graphs ◽  
Disjoint Paths ◽  
Local Connectivity ◽  
Communication Links ◽  
Restricted Condition ◽  
Vertex Disjoint

An interconnection network is usually modeled as a graph, in which vertices and edges correspond to processors and communication links, respectively. Connectivity is an important metric for fault tolerance of interconnection networks. A graph [Formula: see text] is said to be maximally local-connected if each pair of vertices [Formula: see text] and [Formula: see text] are connected by [Formula: see text] vertex-disjoint paths. In this paper, we show that Cayley graphs generated by [Formula: see text]([Formula: see text]) transpositions are [Formula: see text]-fault-tolerant maximally local-connected and are also [Formula: see text]-fault-tolerant one-to-many maximally local-connected if their corresponding transposition generating graphs have a triangle, [Formula: see text]-fault-tolerant one-to-many maximally local-connected if their corresponding transposition generating graphs have no triangles. Furthermore, under the restricted condition that each vertex has at least two fault-free adjacent vertices, Cayley graphs generated by [Formula: see text]([Formula: see text]) transpositions are [Formula: see text]-fault-tolerant maximally local-connected if their corresponding transposition generating graphs have no triangles.

scholarly journals Fault-tolerant Hamiltonian laceability of Cayley graphs generated by transposition trees

2012 ◽  
Vol 312 (21) ◽  
pp. 3087-3095 ◽  
Author(s):  
Hengzhe Li ◽  
Weihua Yang ◽  
Jixiang Meng
Keyword(s):  
Fault Tolerant ◽  
Cayley Graphs ◽  
Hamiltonian Laceability

scholarly journals Distributed and Fault-Tolerant Routing for Borel Cayley Graphs

2012 ◽  
Vol 8 (10) ◽  
pp. 124245 ◽  
Author(s):  
Junghun Ryu ◽  
Eric Noel ◽  
K. Wendy Tang
Keyword(s):  
Interconnection Networks ◽  
Fault Tolerant ◽  
Cayley Graphs ◽  
Routing Algorithm ◽  
Topology Change ◽  
Link Failures ◽  
End To End Delay ◽  
Low Degree ◽  
Transitivity Property ◽  
Path Lengths

We explore the use of a pseudorandom graph family, Borel Cayley graph family, as the network topology with thousands of nodes operating in a packet switching environment. BCGs are known to be an efficient topology in interconnection networks because of their small diameters, short average path lengths, and low-degree connections. However, the application of BCGs is hindered by a lack of size flexibility and fault-tolerant routing. We propose a fault-tolerant routing algorithm for BCGs. Our algorithm exploits the vertex-transitivity property of Borel Cayley graphs and relies on extra information to reflect topology change. Our results show that the proposed method supports good reachability and a small End-to-End delay under various link failures scenarios.

The (E)FTSM-(edge) Connectivity of Cayley Graphs Generated by Transposition Trees

2021 ◽  
pp. 1-11
Author(s):  
Pingshan Li ◽  
Rong Liu ◽  
Xianglin Liu
Keyword(s):  
Cayley Graph ◽  
Fault Tolerant ◽  
Cayley Graphs ◽  
Disjoint Paths ◽  
Star Graph ◽  
Edge Connectivity ◽  
Short Edge ◽  
Edge Disjoint

The Cayley graph generated by a transposition tree [Formula: see text] is a class of Cayley graphs that contains the star graph and the bubble sort graph. A graph [Formula: see text] is called strongly Menger (SM for short) (edge) connected if each pair of vertices [Formula: see text] are connected by [Formula: see text] (edge)-disjoint paths, where [Formula: see text] are the degree of [Formula: see text] and [Formula: see text] respectively. In this paper, the maximally edge-fault-tolerant and the maximally vertex-fault-tolerant of [Formula: see text] with respect to the SM-property are found and thus generalize or improve the results in [19, 20, 22, 26] on this topic.

ANALYSIS OF A CLASS OF NETWORKS BASED ON CUBIC STAR GRAPHS

1994 ◽  
Vol 04 (02) ◽  
pp. 191-222
Author(s):  
S.V.R. MADABHUSHI ◽  
S. LAKSHMIVARAHAN ◽  
S.K. DHALL
Keyword(s):  
Interconnection Networks ◽  
Fault Tolerant ◽  
Cayley Graphs ◽  
Binary Trees ◽  
Star Graph ◽  
Cubic Graphs ◽  
Topological Properties ◽  
Star Graphs ◽  
New Class ◽  
Edge Transitive

A new class of interconnection networks based on a family of graphs, called cubic graphs are introduced. These latter graphs arise as Cayley graphs of certain subgroups of the symmetric group. It turns out that these Cayley graphs are a hybrid between the binary hypercube and the star graph, and hence are called cubic star graphs, and are denoted by CS(m, n), m≥1 and n≥1. CS(m, n) inherits several of the properties of the hypercube and the star graph. In this paper, we present an analysis of the symmetric and topological properties. In particular, it is shown that CS(m, n) is edge transitive and hence maximally fault tolerant. We give an algorithm for finding the shortest path and provide an enumeration of the node disjoint paths. Optimal algorithms for single source and all-source broadcasting (also called gossiping) are derived. It is shown that CS(m, n) is Hamiltonian and interesting embeddings of several cycles, grids, and binary trees are derived. The paper concludes with a comparison of CS(m, n) with the binary hypercube and the star graph.

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