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This project deals with the graph theory topic of taking apart graphs and reassembling them. A graph is a mathematical structure made from vertices, and lines that connect some vertices called edges. Based on the biology problem motivated by the study of self-assmebling DNA nanostructures, this project will look at the basic components, called tiles, that are needed to assemble a graph. Tiles are vertices with branched half-edges. We aim to find the smallest set of different tiles needed to construct certain graphs. Previous research has considered this problem for various types of graphs such as the platonic solids. This project will study the family of graphs made by repeatedly subdividing, or stellating, a face of tetrahedra. We find formulas for the minimum number of tiles needed to assemble this group of graphs.
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Maifeld-Carucci, Iliana Mi'ilani, "Designing DNA Nanostructures: Optimization of Tetrahedra Stellation" (2013). Senior Projects Spring 2013. 409.
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