# ON GRAPHS WITH EQUAL CHROMATIC TRANSVERSAL DOMINATION AND CONNECTED DOMINATION NUMBERS

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

• Published : 2012.10.31
• 27 9

#### 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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