THE DETOUR INDEX

The detour index omega is the sum of all entries in the upper triangle of the detour matrix Delta, where the ij-th entry Delta(ij) denotes t he length of the longest path between vertices i and j of the underlyi ng graph. The Wiener index W and omega are equivalent for acyclic stru ctures, but are different in cycle-containing graphs. Similarly the hy per-Wiener index Gamma and its analogue the hyper-detour index gamma a re equivalent in acyclic structures and are different in cyclic struct ures. Several formulas were derived for omega and gamma. Excellent cor relations between boiling points and the composite indices (W omega)(1 /8) and (Gamma gamma)(1/10) were found in a series consisting of 77 cy clic and acyclic alkanes.