# Self-Assembling DNA Complexes with a Wheel Graph Structure

## TL;DR

This paper explores the design of DNA-based self-assembling complexes modeled by wheel graphs, analyzing the minimal types of DNA tiles needed for assembly under various constraints.

## Contribution

It provides new results on the minimal tile and cohesive-end types required for self-assembling wheel graph structures in different settings.

## Key findings

- Determined minimal tile types for wheel graph assemblies
- Analyzed cohesive-end requirements in multiple settings
- Extended graph theory applications to DNA self-assembly

## Abstract

The Watson-Crick complementary properties of DNA make DNA a useful tool for the self-assembly of various target complexes. Concepts from graph theory can be used to model the self-assembling process in which the vertices of the graph represent $k$-armed branched junction molecules, called tiles. We seek to determine the minimum number of tile and cohesive-end types necessary to create the desired self-assembled complex. Although results are known for a few infinite classes of graphs, many classes of graphs remain unsolved. We present results for the wheel graph within the restrictions of three different settings.