Path Embeddings with Prescribed Edge in the Balanced Hypercube Network

Chen, Dan; Lu, Zhongzhou; Shen, Zebang; Zhang, Gaofeng; Chen, Chong; Zhou, Qingguo

doi:10.3390/sym9060079

Open AccessCommunication

Path Embeddings with Prescribed Edge in the Balanced Hypercube Network

by

Dan Chen

,

Zhongzhou Lu

,

Zebang Shen

,

Gaofeng Zhang

,

Chong Chen

and

Qingguo Zhou

^*

School of Information Science and Engineering, Lanzhou University, Lanzhou, Gansu 730000, China

^*

Author to whom correspondence should be addressed.

Symmetry 2017, 9(6), 79; https://doi.org/10.3390/sym9060079

Submission received: 21 February 2017 / Revised: 21 April 2017 / Accepted: 15 May 2017 / Published: 26 May 2017

(This article belongs to the Special Issue Symmetry in Complex Networks II)

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Abstract

The balanced hypercube network, which is a novel interconnection network for parallel computation and data processing, is a newly-invented variant of the hypercube. The particular feature of the balanced hypercube is that each processor has its own backup processor and they are connected to the same neighbors. A Hamiltonian bipartite graph with bipartition

V_{0} \cup V_{1}

x \in V_{0}

y \in V_{1}

. It is known that each edge is on a Hamiltonian cycle of the balanced hypercube. In this paper, we prove that, for an arbitrary edge

e

in the balanced hypercube, there exists a Hamiltonian path between any two vertices

x

and

y

in different partite sets passing through

e

with

e \neq x y

. This result improves some known results.

Keywords: interconnection network; balanced hypercube; Hamiltonian path; passing prescribed edge; data processing

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MDPI and ACS Style

Chen, D.; Lu, Z.; Shen, Z.; Zhang, G.; Chen, C.; Zhou, Q. Path Embeddings with Prescribed Edge in the Balanced Hypercube Network. Symmetry 2017, 9, 79. https://doi.org/10.3390/sym9060079

AMA Style

Chen D, Lu Z, Shen Z, Zhang G, Chen C, Zhou Q. Path Embeddings with Prescribed Edge in the Balanced Hypercube Network. Symmetry. 2017; 9(6):79. https://doi.org/10.3390/sym9060079

Chicago/Turabian Style

Chen, Dan, Zhongzhou Lu, Zebang Shen, Gaofeng Zhang, Chong Chen, and Qingguo Zhou. 2017. "Path Embeddings with Prescribed Edge in the Balanced Hypercube Network" Symmetry 9, no. 6: 79. https://doi.org/10.3390/sym9060079

APA Style

Chen, D., Lu, Z., Shen, Z., Zhang, G., Chen, C., & Zhou, Q. (2017). Path Embeddings with Prescribed Edge in the Balanced Hypercube Network. Symmetry, 9(6), 79. https://doi.org/10.3390/sym9060079

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Path Embeddings with Prescribed Edge in the Balanced Hypercube Network

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