1-vertex-fault-tolerant Cycles Embedding on Folded Hypercubes

Cycle Embedding in Folded Hypercubes with More Faulty Elements

Faults in a network may take various forms such as hardware/software errors, vertex/edge faults, etc. Folded hypercube is a well-known variation of the hypercube structure and can be constructed from a hypercube by adding a link to every pair of nodes with complementary addresses. Let FFv (respectively, FFe) be the set of faulty nodes (respectively, faulty links) in an n-dimensional folded hype...

Edge-fault-tolerant properties of hypercubes and folded hypercubes

Fault-Free Cycles in Conditional Faulty Folded Hypercubes

An n-dimensional folded hypercube FQn is an attractive variance of an n-dimensional hypercube Qn, which is obtained by a standard hypercube with some extra edges established between its vertices. FQn for any odd n is known to be bipartite. In this paper, for any FQn (n ≥ 2) with at most 2n−3 faulty edges in which each vertex is incident with at least two fault-free edges, we prove that there ex...

On conditional edge-fault-tolerant cycles embedding of hypercubes

The hypercube has been one of the most popular interconnection networks for parallel computer/communication system. In this papers, we assume that each node is incident with at least two fault-free links. Under this assumption, we show that every fault-free edge lies on a fault-free cycle of every even length from 6 to 2 inclusive even if it has up to 2n − 5 link faults. The result is optimal w...

Cayley graphs and symmetric interconnection networks

These lecture notes are on automorphism groups of Cayley graphs and their applications to optimal fault-tolerance of some interconnection networks. We first give an introduction to automorphisms of graphs and an introduction to Cayley graphs. We then discuss automorphism groups of Cayley graphs. We prove that the vertex-connectivity of edge-transitive graphs is maximum possible. We investigate ...