Hocine Boumediene Merouane

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In a graph G, a vertex is said to dominate itself and all its neighbors. A dominating set of a graph G is a subset of vertices that dominates every vertex of G. The domination number γ(G) is the minimum cardinality of a dominating set of G. A proper coloring of a graph G is a function from the set of vertices of the graph to a set of colors such that any(More)
In this paper, we introduce and study a new coloring problem of a graph called the dominated coloring. A dominated coloring of a graph G is a proper vertex coloring of G such that each color class is dominated by at least one vertex of G. The minimum number of colors among all dominated colorings is called the dominated chromatic number, denoted by χdom(G).(More)
A dominator 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 the vertices of at least one color class. The minimum number of colors required for a dominator coloring of G is called the dominator chromatic number of G. In this paper, we give a polynomial time algorithm(More)
In this paper, we are interested in four proper vertex colorings of graphs, with additional domination property. In the dominator colorings, strong colorings and strict strong colorings of a graph G, every vertex has to dominate at least one color class. Conversely, in the dominated colorings of G, every color class has to be dominated by at least one(More)
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