Fault-tolerant Hamiltonian connectivity of 2-tree-generated networks

Abdallah, Mohamad

doi:10.1016/j.tcs.2022.01.020

Cited by 4 publications

(1 citation statement)

References 28 publications

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“…The topological structure of the underlying network can be modeled as a graph where vertices correspond to processors, memory modules or switches, and edges correspond to communication links. It has been universally accepted and used by computer scientists and engineers [1,30].…”

Section: Introductionmentioning

confidence: 99%

Symmetric property and edge-disjoint Hamiltonian cycles of the spined cube

Yang¹,

Zhang²,

Yan³

et al. 2022

Preprint

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The spined cube SQn is a variant of the hypercube Qn, introduced by Zhou et al. in [Information Processing Letters 111 (2011) 561-567] as an interconnection network for parallel computing. A graph Γ is an m-Cayley graph if its automorphism group Aut(Γ) has a semiregular subgroup acting on the vertex set with m orbits, and is a Caley graph if it is a 1-Cayley graph. It is well-known that Qn is a Cayley graph of an elementary abelian 2-group Z n 2 of order 2 n . In this paper, we prove that SQn is a 4-Cayley graph of Z n−2 2 when n ≥ 6, and is a ⌊n/2⌋-Cayley graph when n ≤ 5. This symmetric property shows that an n-dimensional spined cube with n ≥ 6 can be decomposed to eight vertex-disjoint (n − 3)-dimensional hypercubes, and as an application, it is proved that there exist two edge-disjoint Hamiltonian cycles in SQn when n ≥ 4. Moreover, we determine the vertex-transitivity of SQn, and prove that SQn is not vertex-transitive unless n ≤ 3.

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Section: Introductionmentioning

confidence: 99%

Symmetric property and edge-disjoint Hamiltonian cycles of the spined cube

Yang¹,

Zhang²,

Yan³

et al. 2022

Preprint

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Fault-free Hamiltonian paths passing through prescribed linear forests in balanced hypercubes with faulty links

Yang

Song²

2023

Theoretical Computer Science

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On Spanning Wide Diameter of Spider Web Networks

Wang,

Sabir

2024

Parallel Process. Lett.

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For any bipartite graph [Formula: see text] with bipartition [Formula: see text] and [Formula: see text], a [Formula: see text]-container [Formula: see text] is a set of [Formula: see text] internally disjoint paths [Formula: see text] between two vertices [Formula: see text] and [Formula: see text] in [Formula: see text], i.e., [Formula: see text]. Moreover, if [Formula: see text] then [Formula: see text] is called a spanning [Formula: see text]-container, denoted by [Formula: see text]. The length of [Formula: see text] is [Formula: see text]. Besides, [Formula: see text] is spanning [Formula: see text]-laceable if there exists a spanning [Formula: see text]-container between any two vertices [Formula: see text] and [Formula: see text] in [Formula: see text]. Assume that [Formula: see text] and [Formula: see text] are two distinct vertices in a spanning [Formula: see text]-laceable graph [Formula: see text]. Let [Formula: see text] be the collection of all [Formula: see text]’s. Define the spanning [Formula: see text]-wide distance between [Formula: see text] and [Formula: see text] in [Formula: see text], [Formula: see text], and the spanning [Formula: see text]-wide diameter of [Formula: see text], [Formula: see text]. In particular, the spanning wide diameter of [Formula: see text] is [Formula: see text], where [Formula: see text] is the connectivity of [Formula: see text]. In the paper we first provide the lower and upper bounds of the wide diameter of a bipartite graph, and then determine the exact values of the spanning wide diameters of the spider web networks [Formula: see text] for [Formula: see text].

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Fault-tolerant Hamiltonian connectivity of 2-tree-generated networks

Cited by 4 publications

References 28 publications

Symmetric property and edge-disjoint Hamiltonian cycles of the spined cube

Symmetric property and edge-disjoint Hamiltonian cycles of the spined cube

Fault-free Hamiltonian paths passing through prescribed linear forests in balanced hypercubes with faulty links

On Spanning Wide Diameter of Spider Web Networks

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