Real-Number Vertex Invariants and Schultz-Type Indices Based on Eigenvectors of Adjacency and Distance Matrices

Eigenvectors corresponding to the lowest eigenvalue of adjacency and distance matrices are used to generate new real-number local vertex invariants (LOVIs), by applying a Schultz-type algorithm. The intramolecular ordering of vertices was tested. From these LOVIs, several new topological indices have been defined and tested on the basis of intermolecular ordering of isomeric alkanes. Correlation with properties such as the normal boiling temperature and octane numbers have also been studied.