Construction of discrete structures, especially isomers (Q1917329)

The authors consider the problem of enumerating isomers with a given composition. Each isomer corresponds to a graph---the vertices of the graph correspond to the atoms, and the bounds to the linkages---valence 1 for carbon atoms, two for oxygen atoms, one for hydrogen atoms, etc. It is shown how the enumeration subject to constraints reduces to a problem in combinatorial group theory: some actual results are given and various general results proved, in particular the ``gluing lemma'' that relates the groups of two sets of objects to the group of the combined set by an ``outer product'' relation.