Variant Of Hamilton's Icosian Game

Jo-Hanna Ho Wai Yann, (2007) Variant Of Hamilton's Icosian Game. Universiti Malaysia Sabah. (Unpublished)

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Variant of hamilton`s icosian game

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Abstract

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.

Item Type: Academic Exercise
Uncontrolled Keywords: Concentric circles , Icosian game , for Hamiltonian graphs
Subjects: Q Science > QA Mathematics
Divisions: SCHOOL > School of Science and Technology
Depositing User: Noraini
Date Deposited: 09 Jul 2019 23:48
Last Modified: 09 Jul 2019 23:48
URI: http://eprints.ums.edu.my/id/eprint/22527

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