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Branched molecules of deoxyribonucleic acid (DNA) can self-assemble intonanostructures through complementary cohesive strand base pairing. Theproduction of DNA nanostructures is valuable in targeted drug delivery andbiomolecular computing. With theoretical efficiency of laboratory processes inmind, we use a flexible tile model for DNA assembly. We aim to minimize thenumber of different types of branched junction molecules necessary to assemblecertain target structures. We represent target structures as discrete graphsand branched DNA molecules as vertices with half-edges. We present the minimumnumbers of required branched molecule and cohesive-end types under three levelsof restrictive conditions for the tadpole and lollipop graph families. Thesefamilies represent cycle and complete graphs with a path appended via a singlecut-vertex. We include three general lemmas regarding such vertex-induced pathsubgraphs. Through proofs and examples, we demonstrate the challenges that canarise in determining optimal construction strategies.

Tile Based Modeling of DNA Self-Assembly for Two Graph Families with Appended Paths