Variant Of Hamilton's Icosian Game - Jo-Hanna Ho Wai Yann (Universiti Malaysia Sabah, 2007)
This thesis proposes a new way of drawing and finding solutions for Hamiltonian graphs, as well as using them in a variant of Hamilton's original Icosian game. The method involved uses concentric circles to arrange vertices and vertex connections of generally 3 degrees to construct a Hamiltonian graph. Also, a hypothesis that the ratio of vertices to edges in all graphs with these conditions is 2: 3 is proposed. The solutions are found by systematic tracing through circle by circle and back to the point of origin. Analysis for graphs spanning from 9 vertices to 60 vertices were derived and all graphs have a Hamiltonian circuit as well as fulfilling the 2: 3 ratio. It can be concluded that the method of drawing and finding solutions to the Hamiltonian graphs are viable and that all these graphs fulfill the 2: 3 ratio of vertices to edges.