1,137 research outputs found
Fault diagnosability of regular graphs
An interconnection network\u27s diagnosability is an important measure of its self-diagnostic capability. In 2012, Peng et al. proposed a measure for fault diagnosis of the network, namely, the -good-neighbor conditional diagnosability, which requires that every fault-free node has at least fault-free neighbors. There are two well-known diagnostic models, PMC model and MM* model. The {\it -good-neighbor diagnosability} under the PMC (resp. MM*) model of a graph , denoted by (resp. ), is the maximum value of such that is -good-neighbor -diagnosable under the PMC (resp. MM*) model. In this paper, we study the -good-neighbor diagnosability of some general -regular -connected graphs under the PMC model and the MM* model. The main result with some acceptable conditions is obtained, where is the girth of . Furthermore, the following new results under the two models are obtained: for the hierarchical star network , for the split-star networks and for the Cayley graph generated by the -tree
Linearly many faults in 2-tree-generated networks
In this article we consider a class of Cayley graphs that are generated by certain 3-cycles on the alternating group A n . These graphs are generalizations of the alternating group graph A G n . We look at the case when the 3-cycles form a “tree-like structure,” and analyze its fault resiliency. We present a number of structural theorems and prove that even with linearly many vertices deleted, the remaining graph has a large connected component containing almost all vertices. © 2009 Wiley Periodicals, Inc. NETWORKS, 2010Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/64908/1/20319_ftp.pd
Matching preclusion and conditional matching preclusion for bipartite interconnection networks II: Cayley graphs generated by transposition trees and hyper‐stars
The matching preclusion number of a graph with an even number of vertices is the minimum number of edges whose deletion results in a graph that has no perfect matchings. For many interconnection networks, the optimal sets are precisely those induced by a single vertex. It is natural to look for obstruction sets beyond those induced by a single vertex. The conditional matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph with no isolated vertices that has no perfect matchings. In this companion paper of Cheng et al. (Networks (NET 1554)), we find these numbers for a number of popular interconnection networks including hypercubes, star graphs, Cayley graphs generated by transposition trees and hyper‐stars. © 2011 Wiley Periodicals, Inc. NETWORKS, 2011Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/91319/1/20441_ftp.pd
Distributed Corruption Detection in Networks
We consider the problem of distributed corruption detection in networks. In
this model, each vertex of a directed graph is either truthful or corrupt. Each
vertex reports the type (truthful or corrupt) of each of its outneighbors. If
it is truthful, it reports the truth, whereas if it is corrupt, it reports
adversarially. This model, first considered by Preparata, Metze, and Chien in
1967, motivated by the desire to identify the faulty components of a digital
system by having the other components checking them, became known as the PMC
model. The main known results for this model characterize networks in which
\emph{all} corrupt (that is, faulty) vertices can be identified, when there is
a known upper bound on their number.
We are interested in networks in which the identity of a \emph{large
fraction} of the vertices can be identified.
It is known that in the PMC model, in order to identify all corrupt vertices
when their number is , all indegrees have to be at least . In contrast,
we show that in regular-graphs with strong expansion properties, a
fraction of the corrupt vertices, and a fraction of the
truthful vertices can be identified, whenever there is a majority of truthful
vertices. We also observe that if the graph is very far from being a good
expander, namely, if the deletion of a small set of vertices splits the graph
into small components, then no corruption detection is possible even if most of
the vertices are truthful. Finally, we discuss the algorithmic aspects and the
computational hardness of the problem
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