Abstract
Polyenoid systems (or polyenoids) are trees which can be embedded in a hexagonal lattice and represent CnHn+2 polyene hydrocarbons. Complete mathematical solutions in terms of summations and in terms of a generating function are deduced for the numbers of polyenoids when overlapping edges and/or vertices are allowed. Geometrically planar polyenoids (without overlapping vertices) are enumerated by computer programming. Thus the numbers of geometrically nonplanar polyenoids become accessible. Some of their numbers are confirmed by combinatorial constructions, a pen-and-paper method.
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