Chromatic connected domination in graphs. (4th July 2019) - Balamurugan, S.; Anitha, M.; Kalaiselvi, S.
Abstract: Let G = ( V, E ) be a undirected, finite, simple graph. A subset D of V is said to be dominating set if for every v in V – D there exists u in D such that u and v are adjacent. A dominating set D is said to be connected dominating set if < D > has connected. We introduce the concept of chromatic connected dominating set. A subset D of V is said to be chromatic connected dominating set if D is a connected dominating set and χ (< D >) = χ ( G ), where χ ( G ) is a chromatic number of G . The minimum cardinality of chromatic connected dominating set of a graph G is called a chromatic connected domination number and is denoted by γcc ( G ). We find the chromatic connected domination number for some standard graphs and characterize the graph for γcc ( G ) = 2.