A perfect packing of a graph H into a graph G is a spanning subgraph of G whose every component is isomorphic to H. We consider several small graphs H and investigate which fullerene graphs allow such packings. We also consider generalized fullerene graphs and packings of small graphs into classical and generalized fullerenes which are not perfect.
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Finding solutions for problems in chemistry and biology often entails the enumeration of objects within a combinatorial class. Examples include the design space of self-assembling protein or DNA strands and the chemical spaces spanned by a set of chemical reactions modelled as graph transformation rules. Naturally, canonicalisation of objects allows for achieving highly efficient implementations to solve the underlying problem. We will present algorithms, their implementations, and empirical results for
- state-of-the-art canonicalisation of chemical graphs as well as for
- a large-scale enumeration of non-isomorphic 1-face embeddings.
The latter includes pruning techniques based on a novel invariant called bio gap. The likelihood of two segments to bind in a biochemical setting depends on their proximity, and it is conceivable that the proximity might be reflected by the biological gap representation.
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