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.