Date of Submission

Spring 2011

Academic Program

Mathematics

Advisor

Maria Belk

Abstract/Artist's Statement

This project explores the rigidity and flexibility of three-dimensional bar frameworks. A bar framework is a structure consisting of rigid bars connected at joints. The bars may freely move around the joints unless held in place by additional bars. A rigid bar framework is one in which none of the bars may move. Currently there is no complete classi cation for generically rigid bar frameworks in three dimensions. This project works toward such a classi cation by examining powers of cycles and trees, complete bipartite graphs, and graphs with very few vertices and low connectivity. It also explores applications to protein folding and hydrocarbon molecules.

Distribution Options

Dissertation/Thesis

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