A dynamic programming algorithm for simulation of a multi-dimensional torus in a crossed cube

Lai, Chia-Jui; Tsai, Chang-Hsiung; Hsu, Hong-Chun; Li, Tseng-Kui

doi:10.1016/j.ins.2010.08.029

Cited by 12 publications

(3 citation statements)

References 19 publications

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“…As an attractive variant of hypercube, the crossed cube has attracted a great deal of interest [8,[11][12][13]15,16,14,23,24,31,36]. [20] proved that the n-dimensional crossed cube CQ n is not vertex-transitive and [21] showed that the vertex set of CQ n can be divided into 2 ⌈(n−4)/2⌉ equivalence classes, where the vertices in one equivalence class are all similar.…”

Section: Graph Terminology and Notationmentioning

confidence: 99%

Dimension-adjacent trees and parallel construction of independent spanning trees on crossed cubes

Cheng

Fan

Jia

et al. 2013

Journal of Parallel and Distributed Computing

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Section: Graph Terminology and Notationmentioning

confidence: 99%

Dimension-adjacent trees and parallel construction of independent spanning trees on crossed cubes

Cheng

Fan

Jia

et al. 2013

Journal of Parallel and Distributed Computing

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“…Secondly, it is obtained recursively from square and compound cubes in the first way. In the literature, hypercube, and its variants (Folded Hypercube, Crossed Cube and the Hierarchical Cubic Network) have been studied extensively in the interconnection network [1][2][3][4][5][6][7][8][9]. Karcı and Selc ¸uk introduced new hypercube variants and investigated it's Hamilton-like features.…”

Section: Introductionmentioning

confidence: 99%

Connected Square Network Graphs

Selçuk

2022

Universal Journal of Mathematics and Applications

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“…Also, hypercube variants have been derived to ensure the performance increasing of hypercubes. These are the Folded Hypercube ( [2,8]), the Crossed Cube (Twisted Cube) ( [11,14,22]) and the Hierarchical Cubic Network (cf. the survey [1] and [10,17,18]) which are the most popular hypercube variants.…”

Section: Introductionmentioning

confidence: 99%

A new hypercube variant: Fractal Cubic Network Graph

Karcı

Selçuk

2015

Engineering Science and Technology, an International Journal

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a b s t r a c tHypercube is a popular and more attractive interconnection networks. The attractive properties of hypercube caused the derivation of more variants of hypercube. In this paper, we have proposed two variants of hypercube which was called as "Fractal Cubic Network Graphs", and we have investigated the Hamiltonian-like properties of Fractal Cubic Network Graphs FCNG r ðnÞ. Firstly, Fractal Cubic Network Graphs FCNG r ðnÞ are defined by a fractal structure. Further, we show the construction and characteristics analyses of FCNG r ðnÞ where r ¼ 1 or r ¼ 2. Therefore, FCNG r ðnÞ is a Hamiltonian graph which is obtained by using Gray Code for r ¼ 2 and FCNG 1 ðnÞ is not a Hamiltonian Graph. Furthermore, we have obtained a recursive algorithm which is used to label the nodes of FCNG 2 ðnÞ. Finally, we get routing algorithms on FCNG 2 ðnÞ by utilizing routing algorithms on the hypercubes.

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A dynamic programming algorithm for simulation of a multi-dimensional torus in a crossed cube

Cited by 12 publications

References 19 publications

Dimension-adjacent trees and parallel construction of independent spanning trees on crossed cubes

Dimension-adjacent trees and parallel construction of independent spanning trees on crossed cubes

Connected Square Network Graphs

A new hypercube variant: Fractal Cubic Network Graph

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