Planar and Non Planar Construction of ï§- Uniquely Colorable Graph

Authors

  • A. Elakkiya

  • M. Yamuna

How to Cite

Elakkiya, A., & Yamuna, M. (2018). Planar and Non Planar Construction of - Uniquely Colorable Graph. International Journal of Engineering and Technology, 7(4.10), 998-1000. https://doi.org/10.14419/ijet.v7i4.10.26656

Received date: January 29, 2019

Accepted date: January 29, 2019

Published date: October 2, 2018

DOI:

https://doi.org/10.14419/ijet.v7i4.10.26656

Keywords:

Complement, Dual, Non Planar, Planar, Uniquely colorablegraphs.

Abstract

A uniquely colorable graph G whose chromatic partition contains atleast one g - set is termed as a g - uniquely colorable graph. In this paper, we provide necessary and sufficient condition for and G* to be g - uniquely colorable whenever G  g- uniquely colorable and also provide constructive characterization to show that whenever G is g- uniquely colorable such that |P | ³ 2, G can be both planarand non planar.

 

References

  1. [1] Bing Zhou, “On the maximum number of dominating classes in graph coloringâ€, Open Journal of Discrete Mathematics,Vol 6,(2016).pp.70 – 73.

    [2] M. Yamuna, A. Elakkiya, “g - Uniquely colorable graphsâ€, IOPConf. Series: Materials Science and Engineering , Vol.263 ,( 2017).

    [3] M. Yamuna, A. Elakkiya,†Planar graph characterization of g- Uniquely colorable graphsâ€, IOP Conf. Series: Materials Sci-ence and Engineering ,Vol263, ( 2017 ).

    [4] Yamuna, M., Elakkiya, A., “Non domination subdivision stable graphsâ€, IOP Conf. Series: Materials Science and Engineering. Vol 263, ( 2017 ).

    [5] Yamuna, M., Elakkiya, A, “Planar graph characterization of NDSS graphsâ€, IOP Conf. Series: Materials Science and Engineering ,Vol 263 ,( 2017 ).

    [6] Harary, F,Graph Theory, Addison Wesley, Narosa Publishing House, (2001).

    [7] Haynes, T.W., Hedetniemi, S. T & Slater, P. J. Fundamentals of domination in graphs, New York, Marcel Dekker, ( 1998 ).

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How to Cite

Elakkiya, A., & Yamuna, M. (2018). Planar and Non Planar Construction of - Uniquely Colorable Graph. International Journal of Engineering and Technology, 7(4.10), 998-1000. https://doi.org/10.14419/ijet.v7i4.10.26656

Received date: January 29, 2019

Accepted date: January 29, 2019

Published date: October 2, 2018