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Characterizing the polyhedral graphs with positive combinatorial curvature

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. / Graduate

Identiferoai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/8030
Date01 May 2017
CreatorsOldridge, Paul Richard
ContributorsMyrvold, W. J. (Wendy Joanne)
Source SetsUniversity of Victoria
LanguageEnglish, English
Detected LanguageEnglish
TypeThesis
RightsAvailable to the World Wide Web, http://creativecommons.org/licenses/by-nd/2.5/ca/

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