Multiple-Edge-Fault Tolerance with Respect to Hypercubes

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...

A note on edge fault tolerance with respect to hypercubes

In the previous studies on k-edge fault tolerance with respect to hypercubes Qn , matrices for generating linear k-EFT(Qn) graphs were used. Let EFT L(n, k) denote the set of matrices that generate linear k-EFT(Qn) graphs. A matrix in EFT L(n, k) with the smallest number of rows among all matrices in EFT L(n, k) is optimal. We use eftL(n, k) to denote the difference between the number of rows a...

Edge-fault-tolerant properties of hypercubes and folded hypercubes

Edge-fault-tolerant bipanconnectivity of hypercubes

This paper shows that for any two distinct vertices u and vwith distance d in the hypercube Qn (n P 3) with at most 2n 5 faulty edges and each vertex incident with least two faultfree edges, there exist fault-free uv-paths of length ‘ in Qn for every ‘with dþ 4 6 ‘ 6 2 1 and ‘ d 0 ðmod2Þ. This result improves some known results on edge-fault bipanconnectivity of hypercubes. The proof is based o...

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 ...