Tomaž Pisanski: Crossing-equivalence of graph embeddings and polyhedral self-assembly

Povzetek. In a single strand self-assembly by dimers we are usually interested in stable double traces that do not cross at polyhedral vertices. However, when we want to generate all stable double traces it makes sense to group them according to the number of vertex crossings. Using canonical forms we can generate only non-isomorphic ones without any symmetry computations. An equivalence relation among all cellular embeddings of graphs comes handy. We will present some practical tests of our computer programs.