4 research outputs found
On the Orbits of Crossed Cubes
An orbit of is a subset of such that for any two
vertices , where is an isomorphism of . The orbit number of
a graph , denoted by , is the number of orbits of . In [A
Note on Path Embedding in Crossed Cubes with Faulty Vertices, Information
Processing Letters 121 (2017) pp. 34--38], Chen et al. conjectured that
for ,
where denotes an -dimensional crossed cube. In this paper, we
settle the conjecture.Comment: 15 page
Hybrid Fault diagnosis capability analysis of Hypercubes under the PMC model and MM* model
System level diagnosis is an important approach for the fault diagnosis of
multiprocessor systems. In system level diagnosis, diagnosability is an
important measure of the diagnosis capability of interconnection networks. But
as a measure, diagnosability can not reflect the diagnosis capability of
multiprocessor systems to link faults which may occur in real circumstances. In
this paper, we propose the definition of -edge tolerable diagnosability to
better measure the diagnosis capability of interconnection networks under
hybrid fault circumstances. The -edge tolerable diagnosability of a
multiprocessor system is the maximum number of faulty nodes that the system
can guarantee to locate when the number of faulty edges does not exceed
,denoted by . The PMC model and MM model are the two most widely
studied diagnosis models for the system level diagnosis of multiprocessor
systems. The hypercubes are the most well-known interconnection networks. In
this paper, the -edge tolerable diagnosability of -dimensional hypercube
under the PMC model and MM is determined as follows: ,
where , .Comment: 5 pages, 1 figur
Diagnosabilities of regular networks
In this paper, we study diagnosabilities of multiprocessor systems under two
diagnosis models: the PMC model and the comparison model. In each model, we
further consider two different diagnosis strategies: the precise diagnosis
strategy proposed by Preparata et al. and the pessimistic diagnosis strategy
proposed by Friedman. The main result of this paper is to determine
diagnosabilities of regular networks with certain conditions, which include
several widely used multiprocessor systems such as variants of hypercubes and
many others.Comment: 26 page
Relationship between Conditional Diagnosability and 2-extra Connectivity of Symmetric Graphs
The conditional diagnosability and the 2-extra connectivity are two important
parameters to measure ability of diagnosing faulty processors and
fault-tolerance in a multiprocessor system. The conditional diagnosability
of is the maximum number for which is conditionally
-diagnosable under the comparison model, while the 2-extra connectivity
of a graph is the minimum number for which there is a
vertex-cut with such that every component of has at least
vertices. A quite natural problem is what is the relationship between the
maximum and the minimum problem? This paper partially answer this problem by
proving for a regular graph with some acceptable
conditions. As applications, the conditional diagnosability and the 2-extra
connectivity are determined for some well-known classes of vertex-transitive
graphs, including, star graphs, -star graphs, alternating group
networks, -arrangement graphs, alternating group graphs, Cayley graphs
obtained from transposition generating trees, bubble-sort graphs, -ary
-cube networks and dual-cubes. Furthermore, many known results about these
networks are obtained directly