**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**4

# Search results for: Hypercubes

##### 4 Hamiltonian Related Properties with and without Faults of the Dual-Cube Interconnection Network and Their Variations

**Authors:**
Shih-Yan Chen,
Shin-Shin Kao

**Abstract:**

**Keywords:**
Hypercubes,
dual-cubes,
fault-tolerant
hamiltonian property,
dual-cube extensive networks,
dual-cube-like
networks.

##### 3 Independent Spanning Trees on Systems-on-chip Hypercubes Routing

**Authors:**
Eduardo Sant'Ana da Silva,
Andre Luiz Pires Guedes,
Eduardo Todt

**Abstract:**

Independent spanning trees (ISTs) provide a number of advantages in data broadcasting. One can cite the use in fault tolerance network protocols for distributed computing and bandwidth. However, the problem of constructing multiple ISTs is considered hard for arbitrary graphs. In this paper we present an efficient algorithm to construct ISTs on hypercubes that requires minimum resources to be performed.

**Keywords:**
Hypercube,
Independent Spanning Trees,
Networks
On Chip,
Systems On Chip.

##### 2 Cycle Embedding in Folded Hypercubes with More Faulty Elements

**Authors:**
Wen-Yin Huang,
Jia-Jie Liu,
Jou-Ming Chang

**Abstract:**

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 hypercube FQn. Hsieh et al. have shown that FQn - FFv - FFe for n ≥ 3 contains a fault-free cycle of length at least 2n -2|FFv|, under the constraints that (1) |FFv| + |FFe| ≤ 2n - 4 and (2) every node in FQn is incident to at least two fault-free links. In this paper, we further consider the constraints |FFv| + |FFe| ≤ 2n - 3. We prove that FQn - FFv - FFe for n ≥ 5 still has a fault-free cycle of length at least 2n - 2|FFv|, under the constraints : (1) |FFv| + |FFe| ≤ 2n - 3, (2) |FFe| ≥ n + 2, and (3) every vertex is still incident with at least two links.

**Keywords:**
Folded hypercubes,
interconnection networks,
cycle embedding,
faulty elements.

##### 1 The Panpositionable Hamiltonicity of k-ary n-cubes

**Authors:**
Chia-Jung Tsai,
Shin-Shin Kao

**Abstract:**

**Keywords:**
Hamiltonian,
panpositionable,
bipanpositionable,
k-ary n-cube.