Some properties of the topological bond order

The topological bond order is a bond-order-like quantity, put forward in the 1970s. It is defined as p rs T = Z ( G rs ) / Z ( G ) , where G is the molecular graph, Grs is obtained from G by deleting from it the adjacent vertices labelled by r and s, and Z stands for the respective topological (Hosoya) index. Because no easy way for the calculation of p rs T is known, its properties were studied only to a limited degree. We now introduce a modified topological bond order, p ˜ rs T , that can (easily) be calculated from the eigenvalues of G and Grs. For acyclic systems, p ˜ rs T = p rs T . In the case of polycyclic systems a reasonably accurate linear correlation exists between p ˜ rs T and p rs T . Thus, by studying p ˜ rs T the main properties of p rs T can be established.