Two new topological indices based on graph adjacency matrix eigenvalues and eigenvectors

Abstract

The Estrada topological index EE, based on the eigenvalues of the adjacency matrix, is degenerate for cospectral graphs. By additionally considering the eigenvectors, two new topological indices are devised (RV_a and RV_b), which have reduced degeneracy for alkanes or cyclic graphs. Index RV_a shows similarity to EE in ordering of alkanes with 8 to 10 carbon atoms, whereas index RV_b is more similar to the average distance-based connectivity (Balaban index J). Inter-correlations between these four topological indices are discussed, indicating which factors have predominant influence.