The Detour Index

The detour index w is the sum of all entries in the upper triangle of the detour matrix LI, where the ij-th entry Lli} denotes the length of the longest path between vertices i and j of the underlying graph. The Wiener index Wand w are equivalent for acyclic structures, but are different in cycle-containing graphs. Similarly the hyper-Wiener index F and its analogue the hyper-detour index y are equivalent in acyclic structures and are different in cyclic structures. Several formulas were derived for w and y. Excellent correlations between boiling points and the composite indices (Ww)1I8 and (ry)1I10 were found in a series consisting of 77 cyclic and acyclic alkanes.