5 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
Fractional strong matching preclusion for two variants of hypercubes
Let F be a subset of edges and vertices of a graph G. If G-F has no fractional perfect matching, then F is a fractional strong matching preclusion set of G. The fractional strong matching preclusion number is the cardinality of a minimum fractional strong matching preclusion set. In this paper, we mainly study the fractional strong matching preclusion problem for two variants of hypercubes, the multiply twisted cube and the locally twisted cube, which are two of the most popular interconnection networks. In addition, we classify all the optimal fractional strong matching preclusion set of each
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