Harmonious coloring on double star graph families

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Published: Jun 28, 2012
DOI: https://doi.org/10.5556/j.tkjm.43.2012.675
Keywords:
Harmonious coloring central graph middle graph total graph line graph achromatic coloring.

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Vernold Vivin.J
University College of Engineering Nagercoil, Anna University of Technology Tirunelveli (Nagercoil Campus), Nagercoil-629 004.
Venkatachalam M.
Faculty of Engineering, RVS Educational Trust’s Group of Institutions, Coimbatore - 641 402, Tamil Nadu, India.
Kaliraj K.
Department of Mathematics, RVS College of Engineering and Technology, Coimbatore - 641 402, Tamil Nadu, India.

Abstract

In this present paper, we have proved for the line graph of double star graph, the harmonious chromatic number and the achromatic number are equal. As a motivation this work can be extended by classifying the different families of graphs for which these two numbers are equal.

Article Details

How to Cite
Vivin.J, V., M., V., & K., K. (2012). Harmonious coloring on double star graph families. Tamkang Journal of Mathematics, 43(2), 153–158. https://doi.org/10.5556/j.tkjm.43.2012.675
Issue
Vol. 43 No. 2 (2012)
Section
Papers
Author Biographies

Vernold Vivin.J, University College of Engineering Nagercoil, Anna University of Technology Tirunelveli (Nagercoil Campus), Nagercoil-629 004.

Venkatachalam M., Faculty of Engineering, RVS Educational Trust’s Group of Institutions, Coimbatore - 641 402, Tamil Nadu, India.

Kaliraj K., Department of Mathematics, RVS College of Engineering and Technology, Coimbatore - 641 402, Tamil Nadu, India.

References

J. A. Bondy and U.S.R. Murty, Graph theory with Applications, London, MacMillan 1976.

Keith Edwards. A Bibliography of Harmonious Colourings and Achromatic Number.

http://www.computing.dundee.ac.uk/sta/kedwards/biblio.html, 2009.

Frank Harary, Graph Theory, Narosa Publishing home 1969.

Vernold Vivin.J, Ph.D Thesis, Harmonious coloring of total graphs, $n-$leaf, central graphs and circumdetic graphs, Bharathiar University, (2007), Coimbatore, India.

J. Vernold Vivin, M. Venkatachalam and M. M. Akbar Ali, Achromatic coloring on double star graph families,International Journal of Mathematical Combinatorics, 3 (2009), 71--81.