Distances in Molecular Graphs

Abstract

This paper discusses the finding of vertex to vertex distances in molecular graphs. Having found these distances, one can obtain a method for canonical numbering of the atoms in a molecule, which depends on the atomic properties and the distances between equivalence classes. This does not use the traditional Morgan algorithm. Using distances one can also perceive rings. Finally, substructures of interest can be detected using distances between the central atoms of various functional groups. The set of vertex distances are thus a kind of lens for examination of the graph properties of molecules. Applications have thus far been only in organic chemistry. Application to physical chemistry may appear wherever molecular graphs can be helpful, such as in calculations concerning molecules of high symmetry.

Symmetry-Adapted Domination Indices: The Enhanced Domination Sigma Index and Its Applications in QSPR Studies of Octane and Its Isomers

“…They employ the analysis of the Tutte polynomial as a means to extract valuable information regarding the symmetries of a graph. In [2], the authors utilize vertex-to-vertex distances in molecular graphs to uncover symmetry-related properties. These distances provide a method for canonical atom numbering based on atomic properties and equivalence class distances, bypassing the traditional Morgan algorithm.…”