Constructive enumeration of acyclic molecules

Abstract

Simple combinatorial theory of constructive enumeration of rooted trees and trees is suggested. As a byproduct of this approach very simple recursive formulae for numerical (i.e. nonconstructive) enumeration are obtained. The method may be simply generalized for (rooted) trees with edges evaluated by multiplicities and vertices evaluated by alphabetic – atomic symbols. In the process of constructive enumeration the (rooted) trees are represented by unambiguous linear code composed of valences of vertices, edge multiplicities, and atomic symbols assigned to vertices. The elaborated theory may serve as a simple algorithmic background of computer programs for contsructive enumeration of acyclic molecular structures containing heteroatoms and multiple bonds.