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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.29 no.1 Antofagasta May 2010

http://dx.doi.org/10.4067/S0716-09172010000100007 

Proyecciones Journal of Mathematics
Vol. 29, N° 1, pp. 57-76, May 2010.
Universidad Católica del Norte
Antofagasta - Chile


ON HARMONIOUS COLORING OF TOTAL GRAPHS OF C(Cn), C(K1,n) AND C(Pn)


Vernold Vivin J.1
Akbar Ali M. M.1
K. Kaliraj2

1Sri Shakthi Institute Of Engineering And Tech., India
2R. V. S. College Of Engineering And Technology, India



Correspondencia a:


Abstract

In this paper, we present the structural properties of total graph of central graph of cycles Cn, star graphs K1,n and paths Pn denoted by T (C(Cn)), T (C(K1,n)) and T (C(Pn)) respectively. We mainly focus our discussion on the harmonious chromatic number of T (C(Cn)), T (C(K1,n)) and T (C(Pn)).

Keywords : Central graph, total graph and harmonious coloring.

2000 Mathematics Subject Classification : 05C75, 05C15.



References

[1] J. A. Bondy and U.S.R. Murty, Graph theory with Applications, London: MacMillan, (1976).        [ Links ]

[2] Keith Edwards. A Bibliography of Harmonious Colorings and Achromatic Number. http://www.computing.dundee.ac.uk/sta/kedwards/biblio.html, (2009).        [ Links ]

[3] Frank Harary, Graph Theory, Narosa Publishing home, (1969).        [ Links ]

[4] J.Hopcroft and M.S. Krishnamoorthy, On the harmonious coloring of graphs, SIAM J. Algebra Discrete Math 4, pp. 306-311, (1983).        [ Links ]

[5] Marek Kubale, Graph Colorings, American Mathematical Society Providence, Rhode Island, (2004).        [ Links ]

[6] Vernold Vivin. J, Ph.D Thesis, Harmonious Coloring of Total Graphs, n-Leaf, Central graphs and Circumdetic Graphs, Bharathiar University, (2007).        [ Links ]

[7] Vernold Vivin. J and Akbar Ali.M.M, On Harmonious Coloring of Middle Graph of C(Cn), C(K1,n) and C(Pn), Note di Matematica Vol.(29)2, pp. 203-214, (2009).        [ Links ]

Received : December 2009. Accepted : January 2010

Vernold Vivin.J
Department of Mathematics
Sri Shakthi Institute of Engineering and Technology
Coimbatore- 641 062
e-mail : vernold_vivin@yahoo.com


Akbar Ali.M.M
Department of Mathematics
Sri Shakthi Institute of Engineering and Technology
Coimbatore- 641 062
e-mail : um_akbar@yahoo.co.in


K.Kaliraj
Department of Mathematics
R. V. S. College of Engineering and Technology
Coimbatore-641 402
e-mail : k_kaliraj@yahoo.com

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