Molecular graphs, constitutional isomers

The number of connected unlabeled 4-multigraphs on n nodes is not easy to obtain, but obviously satisfies the inequality 

The model used in this book for a chemical compoimd (molecule) is an unlabeled connected colored 4-multigraph, i.e. nodes are colored as described below, eind bond multiplicities are 0,1,2, or 3. 

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Constitutional isomerism is defined as that type of isomerism (i.e., different structures corresponding to the same molecular formula) resulting from differences in vicinity relationships between atoms. Examples of pairs of constitutional isomers are -butane and isobutane [CCCC versus CC(C)C in Smiles notation], ethanol and dimethyl ether (CCO versus COC), 1 - and 2-methylbutene (C=CCC versus CC=CC), and 1- and 2-propanol [CCCO versus CC(0)C]. Constitutional isomerism is adequately accounted for in chemical graph theory by the adjacency or distance matrices, which consider only the vicinity relationships. ... 

On the topological level, we would like to construct all the molecular graphs that correspond to a given molecular formula, the connectivity or constitutional isomers. 

In this book, we shall describe algorithms for solving these problems. The techniques are based on the representation of chemical compounds as molecular graphs, i.e. they are mainly applied to constitutional isomers. 

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