A Note on Chromatic Transversal Weak Domination in Graphs

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2015 by IJMTT Journal
Volume-17 Number-2
Year of Publication : 2015
Authors : S. Balamurugan , P. Selvalakshmi , A. Arivalagan
  10.14445/22315373/IJMTT-V17P512

MLA

S. Balamurugan , P. Selvalakshmi , A. Arivalagan "A Note on Chromatic Transversal Weak Domination in Graphs", International Journal of Mathematics Trends and Technology (IJMTT). V17: 89-95 Jan 2015. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

Abstract
Let G=(V,E) be a graph with chromatic number k. A weak dominating set D of G is called a chromatic transversal weak dominating (ctwd) set if D intersects every colour class of any k-colouring of G. The minimum cardinality of chromatic transversal weak dominating set is called the chromatic transversal Weak domination number of G and it is denoted by γctwd(G). We calculate chromatic transversal weak domination number for some standard graphs and we charecta- rize γctwd(G)=n.

References
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[2]. Sampathkumar.E, and Pushpalatha.L, Strong weak domination and domination balance in a graph, Discrete Math. 161 (1996)235-242. [3] Harary.F: Graph Theory Addison Wesley, reading Mass (1972).
[3]. L.Benedict Michael Raj,S.K. Ayyaswamy and S.Arumugam, Chromatic Transversal Domination in Graphs.
[4]. G.Chartrand and L.Lesniak, Graph and Digraph, Chapman and Hall, CRC, 2005.

Keywords
Domination, Weak domination, Chromatic Number