New Graph Theory applied to Nanoconstruct Design Strategies Joanna Ellis-Monaghan, Professor of Mathematics, Saint Michael's College Greta Pangborn, Associate Professor of Computer Science, Saint Michael's College New work in nanotechnology holds promise for a diverse range of applications, including biomolecular computing, drug delivery, and biosensors (see [Adl94, CS91, LL07, See07]). DNA is an ideal material for building nanostructures because Watson-Crick complementarity allows for molecular self-assembly, in which single strands of DNA bond to complementary strands to form larger molecules. Several different graphs have been constructed from self-assembled DNA molecules, including cubes [CS91], truncated octahedra [ZS94], rigid octahedra [SQJ04], tetrahedra, dodecahedra, and buckyballs [H+08]. A 3D crystalline lattice has also been constructed [Z+09]. Recent origami methods have resulted in DNA self-assembly of 2D images and designs (see [Rot06,HLS09]), and these methods can be translated to 3D structures [DDS09]. We are particularly interested in questions related to optimal design strategies for a number of different self-assembly techniques. For example: What is the minimum number of branched junction molecule types needed to create a particular polytope? What is the best way to thread a polytope or lattice to create the target molecule using a DNA origami technique?