Research on the Hereditary Properties of the Cartesian Product Operation of Graphs

Abstract:

This paper defined the hereditary property (or constant property) concerning graph operation, and discussed various forms of the hereditary property under the circumstance of Cartesian product graph operation. The main conclusions include: The non-planarity and Hamiltonicity of graph are hereditary concerning the Cartesian product, but planarity of graph is not, Euler characteristic and non-hamiltonicity of graph are not hereditary as well. Therefore, when we applied this principle into practice, we testified that Hamilton cycle does exist in hypercube.

• Periodical: Applied Mechanics and Materials (Volumes 241-244)
• Pages: 2802-2806
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.241-244.2802
• Online since: December 2012
• Authors: Hua Dong Wang, Bin Wang, Yan Zhong Hu
• Keywords: Cartesian Product, Hereditary Property, Hypercube

References

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[2] YanZhong Hu, Bo Ye, A Study of Hamilton Cycles in the Direct Sum of a Graph, Journal of Shiyan Technical Institute, Vol.23, No. 3, 2010, pp.103-106(In Chinese).

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

[4] Yanzhong Hu, Huadong Wang, On the Hamilton Cycle of the Hypercube. Key Engineering Materials Vols. 480-481(2011), Trans Tech Publications, Switzerland, pp.922-927.

DOI: 10.4028/www.scientific.net/kem.480-481.922