SOME NEW RESULTS ON CHROMATIC TRANSVERSAL DOMINATION IN GRAPHS

Abstract

A proper k - coloring of a graph G is a function f : V (G) → {1, 2, ..., k} such that f (u) 6 = f (v) for all uv ∈ E(G). The color class Si is the subset of vertices of G that is assigned to color i. The chromatic number χ(G) is the minimum number k for which G admits proper k - coloring. A color class in a vertex coloring of a graph G is a subset of V (G) containing all the vertices of the same color. The set D ⊆ V (G) of vertices in a graph G is called dominating set if every vertex v ∈ V (G) is either an element of D or is adjacent to an element of D. If C = {S1, S2, ..., Sk} is a k - coloring of a graph G then a subset D of V (G) is called a transversal of C if D ∩ Si 6 = φ for all i ∈ {1, 2, ..., k}. A dominating set D of a graph G is called a chromatic transversal dominating set (cdt - set) of G if D is transversal of every chromatic partition of G. Here we prove some characterizations and also investigate chromatic transversal domination number of some graphs.