Advertisement

γ-Chromatic Partition in Planar Graph Characterization

  • M. YamunaEmail author
  • A. Elakkiya
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

A uniquely colorable graph G whose chromatic partition contains at least one γ-set is termed as a γ-uniquely colorable graph. We characterize the planarity of these graphs using the domination number of G.

References

  1. 1.
    Akiyama, J., Harary, F.: A Graph and its Complement with Specified Properties. I: Connectivity, Internat. J. Math Science. 2, 223–228 (1979).Google Scholar
  2. 2.
    Arumugam, A. Ismail Sahul Hamid, I., Muthukamatchi, A.: Independent domination and graph colorings. Proceeding. of ICDM. 195–203 (2006).Google Scholar
  3. 3.
    Battle, B.J., Harary, F., Yukihiro: Every planar graph with nine points has a non planar complement. Communicated by Roger Lyndon. 68, 569–571 (1962).zbMATHGoogle Scholar
  4. 4.
    Bing Zhou: On the maximum number of dominating classes in graph coloring. Open Journal of Discrete Mathematics. 6, 70–73 (2016).Google Scholar
  5. 5.
    Harary, F. 2011. Graph Theory. Addison Wesely, Narosa Publishing House.zbMATHGoogle Scholar
  6. 6.
    Haynes,T. W., Hedetniemi, S. T. and Slater, P. J. 1998. Fundamentals of Domination in Graphs, Marcel Dekker, New York.zbMATHGoogle Scholar
  7. 7.
    Rosa, I., Enciso Ronald, Dutton, D.: Global Domination in Planar Graphs. http://www.cs.ucf.edu/ renciso/Global Domination in Planar Grap.pdf.
  8. 8.
  9. 9.
    Yamuna, M., Karthika,K.: Planar Graph Characterization - Using γ - Stable Graphs, WSEAS Transactions on Mathematics.13, 493–504 (2014).Google Scholar
  10. 10.
    Yamuna, M., Elakkiya, A.: γ - Uniquely colorable graphs, IOP Conf. Series: Materials Science and Engineering. 263 (2017).Google Scholar
  11. 11.
    Yamuna, M., Elakkiya, A.: Planar graph characterization of γ - Uniquely colorable graphs, IOP Conf. Series: Materials Science and Engineering. 263 (2017).Google Scholar
  12. 12.
    Yamuna, M., Elakkiya, A.: Non domination subdivision stable graphs, IOP Conf. Series: Materials Science and Engineering. 263 (2017).Google Scholar
  13. 13.
    Yamuna, M., Elakkiya, A.: Planar graph characterization of NDSS graphs, IOP Conf. Series: Materials Science and Engineering. 263 (2017).Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsVellore Institute of TechnologyVelloreIndia

Personalised recommendations