The Journal of the Indian Mathematical Society

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


Affiliations
1 Department of Mathematics, School of Humanities and Sciences, SASTRA University, Thanjavur-613 401, India
     

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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.

Keywords

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

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

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Authors

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

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.

Keywords


Domination, Colouring, Chromatic Transversal Domination.

References