A generation algorithm for nanojoins

Nanojoins or nanojunctions are substructures of large Carbon molecules that connect two or more nanotubes with the same or different tube parameters. Except in the trivial case where two tubes with the same parameters are connected, nanojoins also contain one or more heptagons in addition to hexagons and possibly pentagons like they also occur in fullerenes and nanotubes. We consider nanojoins as isomorphic when the infinite molecules given by the join connected to infinite tubes are isomorphic. Even when fixing the number of tubes to be connected, the tube parameters, and the number of pentagons and heptagons, there are in most cases infinitely many non-isomorphic nanojoins, so complete enumeration is impossible unless also a parameter restricting the size of the join is added. In this article we describe an algorithm for complete enumeration of non-isomorphic nanojoins for a given set of tube parameters, number of heptagons, and an upper bound on the number of faces in the join. We also give performance statistics and results for some parameter sets.