Abstract
In this paper, we give the definition and construction of the Desargues graph, and illustrate some of its properties like symmetry, hamiltonicity, etc. We put forward and analyze three different methods which are both traditional and innovative to prove the non-planarity of the Desargues graph.
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References
Weisstein, E.W.: "Desargues Graph" from MathWorld
Fan, Y., Wang, Y., Gong, S.: Introduction to Graph Theory, pp. 208–224. Post & Telecon Press, Beijing (2007) (in Chinese)
Li, J., Luo, J.: Introduction to Graph Theory, pp. 8–13. China Machine Press, Beijing (2006) (in Chinese)
Xu, J.: Graph Theory and Its Applications, 2nd edn., pp. 171–175. University of Science and Technology of China Press, Hefei (2004) (in Chinese)
Zhang, X., Li, Z.: Graph Theory and Its Applications, pp. 100–119. Higher Education Press, Beijing (2005) (in Chinese)
Bondy, J.A., Murty, U.S.R.: Graph Theory with Applications, pp. 3–5. Macmillan Press Ltd. (1976)
Diestel, R.: Graph Theory, 3rd edn., Beijing, pp. 101–109 (March 2008), http://www.wpcbj.com.cn
Xie, F., Hu, Y.: Research on the Nonplanarity of the Petersen Graph. In: Proceeding of the International Symposium on Information Engineering and Electronic Commerce, ternopil, ukraine, pp. 215–218 (2010)
Hu, Y., Li, H., Zhou, J.: Research on the Girth of the BC Graph. In: Proceeding of the Intelligent Systems and Applications, Wuhan, pp. 550–553 (2010)
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© 2011 Springer-Verlag Berlin Heidelberg
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Hu, Y., Luo, H. (2011). Study of the Non-planarity of the Desargues Graph. In: Jin, D., Lin, S. (eds) Advances in Computer Science, Intelligent System and Environment. Advances in Intelligent and Soft Computing, vol 106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23753-9_2
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DOI: https://doi.org/10.1007/978-3-642-23753-9_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23752-2
Online ISBN: 978-3-642-23753-9
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