Enumerating Chemical Graphs with Mono-block 2-Augmented Tree Structure from Given Upper and Lower Bounds on Path Frequencies

TL;DR

This paper presents an efficient algorithm for enumerating chemical graphs called 2-augmented trees, based on path frequency constraints, with applications to inverse QSAR/QSPR modeling.

Contribution

The paper introduces a novel algorithm for enumerating chemical 2-augmented trees within specified path frequency bounds, advancing chemical graph enumeration methods.

Findings

Algorithm efficiently enumerates chemical graphs within bounds.

Implemented algorithm successfully in computational experiments.

Supports applications in inverse QSAR/QSPR modeling.

Abstract

We consider a problem of enumerating chemical graphs from given constraints concerning their structures, which has an important application to a novel method for the inverse QSAR/QSPR recently proposed. In this paper, the structure of a chemical graph is specified by a feature vector each of whose entries represents the frequency of a prescribed path. We call a graph a 2-augmented tree if it is obtained from a tree (an acyclic graph) by adding edges between two pairs of nonadjacent vertices. Given a set of feature vectors as the interval between upper and lower bounds of feature vectors, we design an efficient algorithm for enumerating chemical 2-augmented trees that satisfy the path frequency specified by some feature vector in the set. We implemented the proposed algorithm and conducted some computational experiments.