2 research outputs found
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
Lower bounds for dilation, wirelength, and edge congestion of embedding graphs into hypercubes
Interconnection networks provide an effective mechanism for exchanging data
between processors in a parallel computing system. One of the most efficient
interconnection networks is the hypercube due to its structural regularity,
potential for parallel computation of various algorithms, and the high degree
of fault tolerance. Thus it becomes the first choice of topological structure
of parallel processing and computing systems. In this paper, lower bounds for
the dilation, wirelength, and edge congestion of an embedding of a graph into a
hypercube are proved. Two of these bounds are expressed in terms of the
bisection width. Applying these results, the dilation and wirelength of
embedding of certain complete multipartite graphs, folded hypercubes, wheels,
and specific Cartesian products are computed