Paper Titles
Research on Lightning Monitoring System of Solar Photovoltaic Power Generation System
p.117
Novel Plasticity Integration Algorithm in Improved Inverse Analysis Method and its Verification in Clover-Shaped Cup Drawing
p.121
Effect of Nitrogen and Sulphur on the Growth and Qualities of Bunching Onion
p.127
Effect of NH4+-N and NO3--N Ratio on the Growth and Quality of Bunching Onion under High Temperature Stress
p.132
Research on the Non-Planarity about the Tensor Product of Graphs
p.136
Synthesis and Luminescent Characterization of Highlight Blue Mg (II) Materials
p.141
Synthesis and Spectral Characterization of a New Mg (II)-Schiff Base Luminescent Materials
p.145
Preparation of Eu (III) and Tb (III) Complex Materials
p.149
Research on the IR Spectrum and Fluorescence Properties of Cd (II) Complex with 1-Acetyl-2-naphthol-4, 4'-diaminodiphenyl Ether
p.153

Research on the Non-Planarity about the Tensor Product of Graphs

Article Preview

Abstract:

The main purpose of this paper is to study the non-planarity of a graph after the tensor product operation. Introduced the concept of invariant property of graphs concerning some operations. Proved the non-planarity of the graph K3,3 and graph K5 is preserved after the bipartite double cover operation. The main conclusion is that the non-planarity of a graph is a invariant property belonging to the bipartite double cover operation, and hence proved the non-planarity of a graph is preserved after the tensor product operation, and conversely, the planarity of a graph is not preserved after the tensor product operation.

You might also be interested in these eBooks
Advanced Research on Material Engineering, Architectural Engineering and Informatization View Preview

Info:

Periodical:

Advanced Materials Research (Volume 366)

Pages:

136-140

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.366.136

Citation:

Cite this paper

Online since:

October 2011

Authors:

Yan Zhong Hu, Nan Jiang, Hua Dong Wang

Keywords:

Bipartite Double Cover, Invariant Property, Non-Planarity, Tensor Product

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

© 2012 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

References

[1] Reinhard Diestel, Graph Theory 3rd ed, Beijing: www. wpcbj. com. cn, Mar. 2008, p.1–32, p.83–109.

Google Scholar

[2] Lih-Hsing Hsu, Cheng-Kuan Lin, Graph Theory and Interconnection Networks, New York: CRC Press, Sept. 2008, p.161–167.

Google Scholar

[3] Gary Chrtrand, Ping Zhang, Introduction to Graph Theory, Beijing: Post & Telecon Press, Sept. 2007, pp.24-24, 227–253.

Google Scholar

[4] Jianzhong Li, jizhou Luo, Introduction to Graph Theory, Beijing: China Machine Press, Feb. 2006, p.186–214(In Chinese).

Google Scholar

[5] C. Cutvenger, P. Eades, R. Weiskircher. Inserting an edge into a planar[J]. Algorithmica, 2005, 41(4): 289-308.

DOI: 10.1007/s00453-004-1128-8

Google Scholar

[6] N. Bonichon, S. Felsner, M. Mosbah. Convex drawing of 3-connected plane grsphs[J]. Algorithmica, 2007, 47(4): 399-420.

DOI: 10.1007/s00453-006-0177-6

Google Scholar

[7] R. E. L. Aldred, C. Thmoassen. On the maximum number of cycles in a planar[J]. Journal of Graph Theory, 2007, 57: 399-420.

Google Scholar

[8] Graham R. Brightwell and Edward R. Scheinerman. Representations of planar graphs[J]. Journal of Discrete Math., 1993, 6: 214-229.

DOI: 10.1137/0406017

Google Scholar

[9] Dan Archdeacon, C. Paul Bonnington and Charles H. C. Little. An Algebraic characterization of planar graphs[J]. Journal of Graph Theory, 1995, 19: 237-250.

DOI: 10.1002/jgt.3190190209

Google Scholar

[10] Fang Xie, Yanzhong Hu, Research on the Nonplanarity of the Petersen Graph. In: Proceeding of the International Symposium on Information Engineering and Electronic Commerce, ternopil, ukraine, 2010, p.215–218.

DOI: 10.1109/ieec.2010.5533254

Google Scholar

[11] Yanzhong Hu, Hongfang Luo, Study of the Non-planarity of the Desargues Graph. In: Proceeding of the International Symposium on Material Science, Environmental Science and Computer Science, 2011, in press.

Google Scholar