26 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
Cyclic sums, network sharing and restricted edge cuts in graphs with long cycles
Cyclic Sums, Network Sharing and Restricted Edge Cuts in Graphs with Long Cycles
Dieter Rautenbach , Lutz Volkmann
Preprint series: 07-06, 8
MSC 2000
05A17 Partitions of integers
05C40 Connectivity
Abstract
We study graphs G = (V,E) containing a long cycle which for given
integers a1, a2, ..., ak 2 N have an edge cut whose removal results in k
components with vertex sets V1, V2, ..., Vk such that |Vi| ai for 1 i
k. Our results closely relate to problems and recent research in network
sharing and network reliability.
Keywords: restricted edge connectivity, arbitrarily vertex decomposable
graph, network reliability, network sharin