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ON GRAPHS WITH EQUAL CHROMATIC TRANSVERSAL DOMINATION AND CONNECTED DOMINATION NUMBERS

Ayyaswamy, Singaraj Kulandaiswamy;Natarajan, Chidambaram;Venkatakrishnan, Yanamandram Balasubramanian

  • Received : 2011.12.30
  • Published : 2012.10.31

Abstract

Let G = (V, E) be a graph with chromatic number ${\chi}(G)$. 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

References

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