This research investigated three properties related to domination and graph coloring in Graph theory: the domatic number, transitivity number, and Grundy number. Algorithms were written in order to investigate these properties and analyze their various relationships. The algorithms were written in Java and were successfully able to calculate the three properties of random graphs as well as generate graphs with these properties. When analyzing the relationships in 200 random graphs, Tr(G) = Γr(G) in 153 of the random graphs. In 46 of the random graphs, T r(G) = Γr(G) − 1. In one of the random graphs,T r(G) = Γr(G) − 2. This demonstrated the ability to find unique graphs. Precision was measured in order to determine whether the approximation is correct because we are unable to measure accuracy. This does not definitively prove the approximation is correct, but it provides some sense of a confidence metric. Future studies include analyzing the number of edges in relation to the distances between the three properties and using supercomputing to look at these properties for very large graphs with more than 100 vertices. Error can be minimized by improving the upper limit for each specific algorithm. These algorithms can be improved, but they can be used as a method for studying these properties in future research.