Symmetry Properties of Some Chemical Graphs

In the realm of mathematical chemistry, the study of symmetry properties of chemical graphs plays a crucial role in understanding molecular structures. This paper aims to investigate the symmetry characteristics of weighted graphs, specifically as they pertain to Euclidean graphs associated with molecules. Utilizing a straightforward computational method, the authors compute the automorphism groups of these weighted graphs, allowing for a deeper analysis of their symmetry. The effectiveness of this methodology is demonstrated through the application of symmetry calculations on trimethylamine and cubane, showcasing its practicality and efficiency. The findings reveal significant insights into the automorphism groups associated with these chemical structures, contributing to the broader field of graph theory in chemistry. This work not only enhances the foundational understanding of graph-related symmetry in molecular configurations but also provides a useful framework for future analyses of other chemical graphs.