Diagonal Chromatic Number of Maximal Planar Graphs of Diameter Three with Twelve Vertices

This thesis is an exploration of the diagonal chromatic number of maximal planar graphs of diameter less than four. A maximal planar graph is a graph that consists of vertices and edges such that no new edge can be added without intersecting another edge. This thesis will aim to show that if a graph is maximal planar of diameter less than four with twelve vertices then the diagonal chromatic number of the graph is six.