COLORING AND DOMINATION PROBLEMS IN GRAPHS

Each node in the graph G is associated with a single hue, and each color class has a vertex that dominates it. This is what we mean by "domination coloring." . In this work, we demonstrate the strong correlation between the dominant chromatic number and and the overall dominance tally γt(G); and the equivalent for graphs without triangles. For each given graph, we analyze its complexity and show that it is NPcomplete. ≥ 4 and by providing a technique that runs in polynomial time, we may identify networks that ≤ 3. The correlation between the chromatic number of the dominant tone and its relative number of dominant colors chromatic number χ(G), and domination number γ(G). Several graph-theoretic findings are presented, including = χ(G)