International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 279246, 5 pages
http://dx.doi.org/10.1155/2011/279246
Research Article

Equitable Coloring on Total Graph of Bigraphs and Central Graph of Cycles and Paths

J. Vernold Vivin,1 K. Kaliraj,2 and M. M. Akbar Ali3

1Department of Mathematics, University College of Engineering Nagercoil, Anna University of Technology Tirunelveli (Nagercoil Campus), Nagercoil 629 004, Tamil Nadu, India
2Department of Mathematics, R.V.S College of Engineering and Technology, Coimbatore 641 402, Tamil Nadu, India
3Department of Mathematics, Sri Shakthi Institute of Engineering and Technology, Coimbatore 641 062, Tamil Nadu, India

Received 2 December 2010; Accepted 9 February 2011

Academic Editor: Marco Squassina

Copyright © 2011 J. Vernold Vivin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The notion of equitable coloring was introduced by Meyer in 1973. In this paper we obtain interesting results regarding the equitable chromatic number 𝜒 = for the total graph of complete bigraphs 𝑇 ( 𝐾 𝑚 , 𝑛 ) , the central graph of cycles 𝐶 ( 𝐶 𝑛 ) and the central graph of paths 𝐶 ( 𝑃 𝑛 ) .