Dominator Coloring In Graph Theory

The dominator chromatic number χd g is the minimum number of color classes in a dominator coloring of a graph 1. A dominator coloring of a graph g is a proper coloring of g in which.

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A d g coloring of g is any dominator coloring with d g colors.

Dominator coloring in graph theory. The dominator chromatic number d g is the minimum number of color classes in a dominator coloring of a graph g. Every vertex dominates every vertex of at least one color class. The minimum number of colors required for a dominator coloring ofg is called thedominator chromatic number.

The dominator chromatic number χd g is the minimum number of color classes in a dominator coloring of. In this paper we obtain the exact value. Development of graph theory and more generally discrete mathematics and combinatorial optimization.

Total dominator coloring of a vague graph g is a coloring of the vertices of g such that every vertex totally dominates all vertices of at least one other class. Colors required for a dominator coloring of g is called the dominator chromatic number. A dominator coloring dc is a coloring of the vertices of a graph such that every vertex is either alone in its color class or adjacent to all vertices of at least one other class.

The minimum number of. A dominator coloring of a graph g is a proper coloring of g such that closed neighborhood of each vertex of g contains a color class of the minimum number of colors required for a dominator coloring of g is called the dominator chromatic number of g denoted by. A dominator coloring of a graph g is a coloring of g in which every vertex dominates every vertex of at least one color class.

A graph has a dominator coloring if it has a proper coloring in which each vertex of the graph dominates every vertex of some color class. The total dominator chromatic number χd t g of g is the minimum number of colors among all total dominator colorings of g. A dominator coloring of a graph g is a proper coloring in which each vertex of the graph dominates every vertex of some color class.

A graph has a dominator coloring if it has a proper coloring in which each vertex of the graph dominates every vertex of some color class. Of g and is denoted by χd g.

An Example Of A Vague Graph G Download Scientific Diagram