Communications of the
Korean Mathematical Society CKMS

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Commun. Korean Math. Soc. 2012; 27(4): 843-849

Printed December 1, 2012

https://doi.org/10.4134/CKMS.2012.27.4.843

Copyright © The Korean Mathematical Society.

On graphs with equal chromatic transversal domination and connected domination numbers

Singaraj Kulandaiswamy Ayyaswamy, Chidambaram Natarajan, and Yanamandram Balasubramanian Venkatakrishnan

SASTRA University, SASTRA University, SASTRA University

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Let $G=(V,E)$ be a graph with chromatic number $\chi(G)$. A dominating set $D$ of $G$ is called a chromatic transversal dominating set (ctd-set) if $D$ intersects every color class of every $\chi$-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 $\gamma_{ct}(G)$. In this paper we characterize the class of trees, unicyclic graphs and cubic graphs for which the chromatic transversal domination number is equal to the connected domination number.

Keywords: domination number, connected domination number, chromatic transversal domination number

MSC numbers: 05C69, 05C75

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