DNA self-assembly, DNA tiles, tile based assembly, branched junction molecules, spectrum of a pot, lattice graph, platonic solid
A design goal in self-assembly of DNA nanostructures is to find minimal sets of branched junction molecules that will self-assemble into targeted structures. This process can be modeled using techniques from graph theory. This paper is a collection of proofs for a set of DNA complexes which can be represented by specific graphs, namely Platonic solids, square lattice graphs, and triangular lattice graphs. This work supplements the results presented in https://arxiv.org/abs/2108.00035
Almodovar, Leyda; Ellis-Monaghan, Joanna; Harsy, Amanda; Johnson, Cory; and Sorrells, Jessica, "Optimal Tile-Based DNA Self-Assembly Designs for Lattice Graphs and Platonic Solids" (2021). Mathematics Faculty Publications. 1.