Variant Of Hamilton's Icosian Game

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 (Unpublished)

Other Variant of hamilton`s icosian game Download (902kB)

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
Keyword:	Concentric circles , Icosian game , for Hamiltonian graphs
Subjects:	Q Science > QA Mathematics
Department:	SCHOOL > School of Science and Technology
Depositing User:	NORAINI LABUK -
Date Deposited:	10 Jul 2019 07:48
Last Modified:	10 Jul 2019 07:48
URI:	https://eprints.ums.edu.my/id/eprint/22527

Actions (login required)

View Item