Topological Aspect of DNA Cages: Genus

DNA cages are kind of artificial polyhedra that are interlinked and interlocked with DNA double-strands. A simple formula to calculate genus of DNA cages is presented here. The formula connects some topological properties of DNA cages, including component number μ, crossing number c and Seifert circle number s. It shows that no matter the way of DNA strands interlinked, the genus is a constant which only depends on the component number of the underlying polyhedral graph. Our study demonstrates that, the genus is an essential topological aspect of DNA polyhedra, which provides a novel classification and a design principle for DNA cages.

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