Algorithmic approximations to Transitivity Numbers and other graph invariance related to domination
Let G = (V, E) be a graph with a set of vertices V and a set of edges E. Graph coloring is assigning some color to separate the vertices of the graph into different sets, creating a partition. A dominating set is a set of vertices where the collective vertices of that set are adjacent to every vertex not in the set. A domatic partition is one in which every set of vertices in a graph is dominating. The transitivity number is the maximum number of sets where each set dominates all successive one. The Grundy number is similar to transitivity but no two vertices of the same set can be adjacent. This research investigated implementing algorithms to generate these partitions and calculate the transitivity number, Grundy number, and domatic number of any graph.