On Symmetry of Some Non-transitive Chemical Graphs

The automorphism group of a chemical graph must be generated for computer-aided structure elucidation. This paper defines a Euclidean graph associated with a molecule as a weighted graph with an adjacency matrix representing the Euclidean distances between the nuclei. The study discusses a methodology to calculate the automorphism group of weighted graphs, inspired by earlier works on monster graphs and complexity indices. By employing group theory, the authors explore the connection between molecular symmetry and theoretical constructs in graph theory. The findings indicate that while molecular symmetry is crucial for understanding the properties of compounds, the existing methods involve considerable calculations. This work proposes a simpler approach, potentially facilitating the analysis of chemical structures by calculating their automorphism groups more efficiently. The implications of this methodology can lead to improved techniques for interpreting experimental data related to molecular symmetry. This research uniquely combines mathematical theory and chemical applications, aiming to bridge the disciplines of chemistry and mathematics for enhanced structural analysis.