Geometric representations of distinct Hamiltonian circuits in complete graph decomposition

• Main Author: Maizon, Mohd Darus
• Format: Thesis
• Language: English; English
• Published: 2015
• Subjects: QA Mathematics
• Online Access: http://etd.uum.edu.my/5322/; http://sierra.uum.edu.my/record=b1272239~S1

Visualization of geometric representations of distinct Hamiltonian circuits in complete graphs is needed to avoid structures resemblance in real application. However, there are only a few studies that consider graph visualization, whereas most researchers focus on computation time. Thus, this study aims to construct a novel picturing method called Half Butterfly Method (HBM) to address the aforementioned scenario. Towards developing HBM, the concept of Wing Strategy is introduced to create directions from one vertex to another vertex. Then, these directions are used to map distinct vertices. In order to obtain the distinct Hamiltonian circuits, the concept of matrix transpose is used to capture the mirror image of that circuit. Several new theorems and lemmas are proved in the decomposition of complete graphs into distinct Hamiltonian circuits. Furthermore, the result of HBM is applied to list.