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) ...

If G is a graph with vertex set V (G) then dominating set D⊆ V (G) is called total if every vertex of V (G) is adjacent to at least one vertex of D while it is called equitable if for every vertex u in V (G)− D there exists ...

A vertex dominating set D of V (G) is called a chromatic transversal dominating set of G if D intersects every color class of G. The minimum cardinality of D is called a chromatic transversal domination number of G. In ...