A Note on the Chromatic Transversal Domination Number of a Class of Graphs

Jump To References Section

Authors

  • C. Natarajan
     Department of Mathematics, School of Humanities and Sciences, SASTRA University, Thanjavur-613 401 ,IN
  • S. K. Ayyaswamy
     Department of Mathematics, School of Humanities and Sciences, SASTRA University, Thanjavur-613 401 ,IN

Keywords:

Domination, Colouring, Chromatic Transversal Domination.

Abstract

Let G = (V, E) be a graph with chromatic number Χ(G). A dominating set D of G is called a chromatic transversal dominating set (ctd-set, in short) if D intersects every colour class of every Χ-partition of G. The minimum cardinality of a ctd-set of G is called the chromatic transversal domination number of G and is denoted by ϒct(G). In this paper we solve a few open problems pertaining to this parameter for Shadow graph and Mycielskian graph of any graph G.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Downloads

Published

2016-12-01

How to Cite

Natarajan, C., & Ayyaswamy, S. K. (2016). A Note on the Chromatic Transversal Domination Number of a Class of Graphs. The Journal of the Indian Mathematical Society, 83(3-4), 323–328. Retrieved from https://informaticsjournals.co.in/index.php/jims/article/view/6612

Issue

Volume 83, Issue 3-4, July-December 2016

Section

Articles

License

Copyright (c) 2016 C. Natarajan, S. K. Ayyaswamy

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

 

References

S. Arumugam, K. Raja Chandrasekar, On chromatic transversal domination in graphs, Journal of Combinatorial Mathematics and Combinatorial Computing, 83, pp.13-21(2012).

R. Balakrishnan and K. Ranganathan, A Textbook of Graph Theory, second edition, Universitext,Springer, 2012.

L. Benedict Michaelraj, S.K. Ayyaswamy and S. Arumugam, Chromatic transversal domination in graphs, Journal of Combinatorial Mathematics and Combinatorial Computing, 75, pp.33-40(2010).

L. Benedict Michaelraj, S.K. Ayyaswamy and I. Sahul Hamid, Chromatic Transversal Domatic number of graphs, International Mathematical Forum, 5(13), pp.639-648(2010).

L. Benedict Michaelraj and S.K. Ayyaswamy, Some Characterization Theorems on Dominating Chromatic Partition-Covering number of graphs, 33(1), pp.13-23(2014).

L. Benedict Michaelraj, A Study on Chromatic Transversal Domination in graphs; (Ph.D Thesis), Bharathidasan University, Trichy, Tamilnadu, India, April 2008. Chapman and Hall, CRC, 4th edition (2005).

T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, New York (1998).