The Operations Invariant Properties on Graphs

DOI

10.2991/icetis-13.2013.51How to use a DOI?

Keywords

Invariant property; Hamilton cycle; Cartesian product; Tensor product

Abstract

To determine whether or not a given graph has a Hamilton cycle (or is a planar graph), defined the operations invariant properties on graphs, and discussed the various forms of the invariant properties under the circumstance of Cartesian product graph operation and Tensor product graph operation. The main conclusions include: The Hamiltonicity of graph is invariant concerning the Cartesian product, and the non-planarity of the graph is invariant concerning the tensor product. Therefore, when we applied these principles into practice, we testified that Hamilton cycle does exist in hypercube and the Desargues graph is a non-planarity graph.

Copyright

© 2013, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Yanzhong Hu
AU  - Gang Cheng
PY  - 2013/06
DA  - 2013/06
TI  - The Operations Invariant Properties on Graphs
BT  - Proceedings of the 2013 the International Conference on Education Technology and Information System (ICETIS 2013)
PB  - Atlantis Press
SP  - 231
EP  - 235
SN  - 1951-6851
UR  - https://doi.org/10.2991/icetis-13.2013.51
DO  - 10.2991/icetis-13.2013.51
ID  - Hu2013/06
ER  -