A Note on Chromatic Transversal Weak Domination in Graphs

S. Balamurugan; P. Selvalakshmi; A. Arivalagan

doi:https://doi.org/10.14445/22315373/IJMTT-V17P512

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 17 | Number 2 | Year 2015 | Article Id. IJMTT-V17P512 | DOI : https://doi.org/10.14445/22315373/IJMTT-V17P512

A Note on Chromatic Transversal Weak Domination in Graphs

S. Balamurugan, P. Selvalakshmi, A. Arivalagan

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.

Keywords

Domination, Weak domination, Chromatic number

References

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[4] L.Benedict Michael Raj,S.K. Ayyaswamy and S.Arumugam, Chromatic Transversal Domination in Graphs.
[5] G.Chartrand and L.Lesniak, Graph and Digraph, Chapman and Hall, CRC, 2005.

Citation :

S. Balamurugan, P. Selvalakshmi, A. Arivalagan, "A Note on Chromatic Transversal Weak Domination in Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 17, no. 2, pp. 89-95, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V17P512