Edge-connectivity indices in QSPR/QSAR studies. 2. Accounting for long-range bond contributions

A novel graph theoretical polynomial, P-epsilon(G,x), counting the edge con nectivity is introduced. The first derivative of this polynomial evaluated for x = 0 is equal to the edge-connectivity index of the molecular graph. A series of edge-connectivity indices modified to include long-range bond co ntributions, epsilon(c)(x), are obtained by using values of x different fro m zero. These indices form three independent (orthogonal) groups containing different structural information as proved by the principal component anal ysis. The use of the epsilon(c)(x) indices in QSPR studies produced signifi cant improvements in the statistical results compared to the original edge- connectivity index, epsilon, for six of the seven properties studied. Some of the novel descriptors are able to describe physicochemical properties po orly correlated to the original epsilon index.