Characterizing the polyhedral graphs with positive combinatorial curvature
| dc.contributor.author | Oldridge, Paul Richard | |
| dc.contributor.supervisor | Myrvold, W. J. (Wendy Joanne) | |
| dc.date.accessioned | 2017-05-01T15:05:35Z | |
| dc.date.available | 2017-05-01T15:05:35Z | |
| dc.date.copyright | 2017 | en_US |
| dc.date.issued | 2017-05-01 | |
| dc.degree.department | Department of Computer Science | en_US |
| dc.degree.level | Master of Science M.Sc. | en_US |
| dc.description.abstract | A polyhedral graph G is called PCC if every vertex of G has strictly positive combinatorial curvature and the graph is not a prism or antiprism. In this thesis it is shown that the maximum order of a 3-regular PCC graph is 132 and the 3-regular PCC graphs which match that bound are enumerated. A new PCC graph with two 39-faces and 208 vertices is constructed, matching the number of vertices of the largest PCC graphs discovered by Nicholson and Sneddon. A conjecture that there are no PCC graphs with faces of size larger than 39 is made, along with a proof that if there are no faces of size larger than 122, then there is an upper bound of 244 on the order of PCC graphs. | en_US |
| dc.description.scholarlevel | Graduate | en_US |
| dc.identifier.uri | http://hdl.handle.net/1828/8030 | |
| dc.language | English | eng |
| dc.language.iso | en | en_US |
| dc.rights | Available to the World Wide Web | en_US |
| dc.rights.uri | http://creativecommons.org/licenses/by-nd/2.5/ca/ | * |
| dc.subject | combinatorial curvature | en_US |
| dc.subject | positive combinatorial curvature | en_US |
| dc.subject | PCC | en_US |
| dc.subject | polyhedral graph | en_US |
| dc.subject | polyhedron | en_US |
| dc.title | Characterizing the polyhedral graphs with positive combinatorial curvature | en_US |
| dc.type | Thesis | en_US |