Application of graph theory to the well-known complementary properties of DNA strands has resulted in new insights about more efficient ways to form DNA nanostructures, which have been discovered as useful tools for drug delivery, biomolecular computing, and biosensors. The key concept underlying DNA nanotechnology is the formation of complete DNA complexes out of a given collection of branched junction molecules. These molecules can be modeled in the abstract as portions of graphs made up of vertices and half-edges, where complete edges are representations of double-stranded DNA pieces that have joined together. For efficiency, one aim is to minimize the number of different component molecules needed to build a nanostructure. Previously known flexible strand model results include optimal construction solutions for cycles, trees, complete graphs, and complete bipartite graphs. In this work, we provide results for all sizes of gear graphs within the context of three different restrictive conditions
