Optimal Embeddings of Paths with Various Lengths in Twisted Cubes

Optimal fault-tolerant embedding of paths in twisted cubes

The twisted cube is an important variation of the hypercube. It possesses many desirable properties for interconnection networks. In this paper, we study fault-tolerant embedding of paths in twisted cubes. Let TQn(V,E) denote the n-dimensional twisted cube. We prove that a path of length l can be embedded between any two distinct nodes with dilation 1 for any faulty set F ⊂ V (TQn)∪E(TQn) with ...

Embeddings of hamiltonian paths in faulty k-ary 2-cubes

It is well known that the k-ary n-cube has been one of the most efficient interconnection networks for distributed-memory parallel systems. A k-ary n-cube is bipartite if and only if k is even. Let (X,Y ) be a bipartition of a k-ary 2-cube (even integer k ≥ 4). In this paper, we prove that for any two healthy vertices u ∈ X, v ∈ Y , there exists a hamiltonian path from u to v in the faulty k-ar...

Optimal Embedding of Locally Twisted Cubes into Grids

Paths in Möbius cubes and crossed cubes

The Möbius cube MQn and the crossed cube CQn are two important variants of the hypercube Qn. This paper shows that for any two different vertices u and v in G ∈ {MQn,CQn} with n 3, there exists a uv-path of every length from dG(u, v)+ 2 to 2n − 1 except for a shortest uv-path, where dG(u, v) is the distance between u and v in G. This result improves some known results.  2005 Elsevier B.V. All ...

Panconnectivity of locally twisted cubes

The locally twisted cube LTQn which is a newly introduced interconnection network for parallel computing is a variant of the hypercube Qn . Yang et al. [X. Yang, G.M. Megson, D.J. Evans, Locally twisted cubes are 4-pancyclic, Applied Mathematics Letters 17 (2004) 919–925] proved that LTQn is Hamiltonian connected and contains a cycle of length from 4 to 2 n for n ≥ 3. In this work, we improve t...