ON GRAPHS WITH EQUAL CHROMATIC TRANSVERSAL DOMINATION AND CONNECTED DOMINATION NUMBERS

Title & Authors
ON GRAPHS WITH EQUAL CHROMATIC TRANSVERSAL DOMINATION AND CONNECTED DOMINATION NUMBERS
Ayyaswamy, Singaraj Kulandaiswamy; Natarajan, Chidambaram; Venkatakrishnan, Yanamandram Balasubramanian;

Abstract
Let G = (V, E) be a graph with chromatic number $\small{{\chi}(G)}$. dominating set D of G is called a chromatic transversal dominating set (ctd-set) if D intersects every color class of every $\small{{\chi}}$-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 $\small{{\gamma}_{ct}}$(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;
Language
English
Cited by
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