Pruning the search tree in the constructive enumeration of molecular graphs Original Research Article

Exhaustive and nonredundant constructive enumeration of molecular graphs (vertex colored multigraphs) with possible further constraints such as prescribed valence states of atoms (degrees of each vertex for each edge multiplicity) is presented. The employed canonical labeling of vertices is based on maximum code formed from the rows of the upper-triangle part of the adjacency matrix concatenated in a sequence from the top to the bottom. The recurrent constructive scheme uses several techniques for rejection of subtrees of a search tree, such as checking conditions for sequences of valence states to be graphical and employing of the automorphism group. The description is accompanied by illustrative examples.