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

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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.