The Johnson solids are the 92 three-dimensional, convex solids (other than the Platonic and Archimedean solids) that can be formed with regular polygons. The purpose of this honor’s thesis work is to determine the toughness of some of the Johnson Solids and similar graphs. The Johnson solids can be broken up into classes of solids with certain characteristics. While there are only 92 Johnson solids in three dimensions, we can generate infinite classes of graphs in two dimensions with similar characteristics. We have identified some of these classes, studied the toughness of individual graphs and begun to analyze a few classes of graphs. Many different techniques from a variety of sources have been employed to explore the toughness of these graphs. We have achieved bounds for toughness in some of these classes and look to prove exact results.
Ward Heilman (Thesis Advisor)
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Original document was submitted as an Honors Program requirement. Copyright is held by the author.
Koval, Sean. (2018). On the Toughness of Some Johnson Solids. In BSU Honors Program Theses and Projects. Item 281. Available at: https://vc.bridgew.edu/honors_proj/281
Copyright © 2018 Sean Koval