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Abstract

The unique properties of double-stranded DNA molecules make DNA a valuable structural material with which to form nanostructures, and the field of DNA nanotechnology is largely based on this premise. By modeling nanostructures with discrete graphs, efficient DNA self-assembly becomes a mathematical puzzle. These nanostructures have wide-ranging applications, such as containers for the transport and release of nano-cargos, templates for the controlled growth of nano-objects, and in drug-delivery methods. This research centers around exploring graph theoretical and combinatorial properties of DNA self-assembly to optimize the nanostructure construction for the Double Cone Graph.

Author Bio

Philiffe Tebalan is an undergraduate student at Lewis University with a major in Mathematics and a minor in Computer Engineering. At Lewis, a Lasallian university located outside of Chicago, he spent time conducting research on graph theoretical modeling of self-assembling DNA, looking at specific graphs such as the double cone graph and the fan graph. He presented this research at several conferences, including the 2024 MMA Mathfest. Outside of his studies, he enjoys reading, drawing, and playing online games with his friends.

Evan Burns is an undergraduate student at Lewis University, a four-year, private, Lasallian university located outside of Chicago, who is studying mathematics and computer science. Evan likes to be a part of mathematics research with his peers and mentors. Evan has taken a plethora of advanced math courses, such as complex analysis, probability theory, and differential equations. Evan has given presentations for his research at events at Lewis such as the SURE research symposium. Evan has also participated in giving a presentation at the 2024 MAA MathFest conference for his research.

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