569 research outputs found
Edge-Fault Tolerance of Hypercube-like Networks
This paper considers a kind of generalized measure of fault
tolerance in a hypercube-like graph which contain several well-known
interconnection networks such as hypercubes, varietal hypercubes, twisted
cubes, crossed cubes and M\"obius cubes, and proves for any with by the induction on
and a new technique. This result shows that at least edges of
have to be removed to get a disconnected graph that contains no vertices of
degree less than . Compared with previous results, this result enhances
fault-tolerant ability of the above-mentioned networks theoretically
Fault-tolerant analysis of augmented cubes
The augmented cube , proposed by Choudum and Sunitha [S. A. Choudum, V.
Sunitha, Augmented cubes, Networks 40 (2) (2002) 71-84], is a -regular
-connected graph . This paper determines that the 2-extra
connectivity of is for and the 2-extra
edge-connectivity is for . That is, for
(respectively, ), at least vertices (respectively,
edges) of have to be removed to get a disconnected graph that contains
no isolated vertices and isolated edges. When the augmented cube is used to
model the topological structure of a large-scale parallel processing system,
these results can provide more accurate measurements for reliability and fault
tolerance of the system
Calculus III: Taylor Series
We study functors from spaces to spaces or spectra that preserve weak
homotopy equivalences. For each such functor we construct a universal
n-excisive approximation, which may be thought of as its n-excisive part.
Homogeneous functors, meaning n-excisive functors with trivial (n-1)-excisive
part, can be classified: they correspond to symmetric functors of n variables
that are reduced and 1-excisive in each variable. We discuss some important
examples, including the identity functor and Waldhausen's algebraic K-theory.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol7/paper19.abs.htm
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