… we introduce and study a new coloring problem of a graph called the dominated coloring.
A … all dominating vertices. We define a new coloring that we call the dominated coloring as …

… dominated coloring of G is called the dominated chromatic number of G, denoted by χdom(G).
In this paper, dominated coloring of graphs … shown that if G is a graph of order n with diam(…

… in four proper vertex colorings of graphs, with additional domination property. In the …
colorings, strong colorings and strict strong colorings of a graph G , every vertex has to dominate at …

… For any dominator coloring (dominated coloring) of G, we can get a dominating set by taking
a vertex in each color class. Thus, γ ( G ) ≤ max { χ d ( G ) , χ d o m ( G ) } . Therefore, the left …

… Graph coloring and domination are two major areas in graph theory that have been well
studied. An excellent treatment of fundamentals of domination is given in the book by Haynes et …

… such a vertex x i is a b-dominating vertex of the color i and that a coloring satisfying P is a
b-dominating coloring. The set { x 1 , x 2 , … , x ϕ ( G ) } will be called a b-dominating system. …

… classical problems, namely Coloring and Domination, … coloring of a graph G is an assignment
of colors to the vertices of G such that it is a proper coloring and every vertex dominates all …

… number \(\gamma _t(G)\) of \(G\) is the minimum cardinality of a total dominating set of \(G\). …
of a graph in terms of its total domination number. In particular, we show that every graph \(G\…

… total dominating colorings in planar graphs of small diameter, where the diameter of a graph
G … results on the domination and total domination numbers of such graphs, especially for the …

… As mentioned earlier, there are some classes of graphs for … -dominating set problem
and the list edge-q-coloring problem (… graphs, distance hereditary graphs, and (q′,q′−3)-graphs …