Optimal Tilings of Bipartite Graphs Using Self-Assembling DNA

Authors

  • Eric Redmon Lewis University
  • Miles Mena Lewis University
  • Megan Vesta Lewis University
  • Alvi Renzyl Cortes Lewis University
  • Lauren Gernes Lewis University
  • Simon Merheb Lewis University
  • Nick Soto Lewis University
  • Chandler Stimpert Lewis University
  • Amanda Harsy Lewis University

DOI:

https://doi.org/10.46787/pump.v6i0.2427

Keywords:

graph theory; self-assembling DNA; tiling; nanotechnology; bipartite graphs

Abstract

Motivated by the recent advancements in nanotechnology and the discovery of new laboratory techniques using the Watson-Crick complementary properties of DNA strands, formal graph theory has recently become useful in the study of self-assembling DNA complexes. Construction methods based on graph theory have resulted in significantly increased efficiency. We present the results of applying graph theoretical and linear algebra techniques for constructing crossed-prism graphs, crown graphs, book graphs, stacked book graphs, and helm graphs, along with kite, cricket, and moth graphs. In particular, we explore various design strategies for these graph families in two sets of laboratory constraints.

Author Biographies

Eric Redmon, Lewis University

Lewis University undergraduate student, class of 2020, primary undergraduate author, currently a graduate student at Marquette University.

Miles Mena, Lewis University

Lewis University undergraduate student, class of 2023.

Megan Vesta, Lewis University

Lewis University undergraduate, class of 2023.

Alvi Renzyl Cortes, Lewis University

Lewis University undergraduate student, class of 2019.

Lauren Gernes, Lewis University

Lewis University undergraduate student, class of 2021.

Simon Merheb, Lewis University

Lewis University undergraduate student.

Nick Soto, Lewis University

Lewis University undergraduate student, class of 2019.

Chandler Stimpert, Lewis University

Lewis University undergraduate student, class of 2019. Currently a graduate student at University of Texas Austin.

Amanda Harsy, Lewis University

Dr. Amanda Harsy is an Associate Professor of Mathematics at Lewis University, a four-year, private, Lasallian university located in Romeoville, Illinois, 35 miles southwest of Chicago. She is also part of the leadership team for the Southwest Chicago Suburbs Math Teachers’ Circle. She enjoys mentoring undergraduate research and has worked with over 35 students on projects involving math education, linear algebra, graph theory, spots analytics, and data science. Dr. Harsy is an active member of the greater mathematical community and has served as the ISMAA's Director of Private Colleges and the Secretary/Treasurer of the MAA Sports SIGMAA. 

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Published

2023-03-13

How to Cite

Redmon, E., Mena, M., Vesta, M., Renzyl Cortes, A., Gernes, L., Merheb, S., … Harsy, A. (2023). Optimal Tilings of Bipartite Graphs Using Self-Assembling DNA. The PUMP Journal of Undergraduate Research, 6, 124–150. https://doi.org/10.46787/pump.v6i0.2427