Mean Wiener Numbers and Other Mean Extensions for Alkane Trees

The "Wiener number" (the sum over intersite graph distances of a structure) as averaged over all alkane structural isomers of a fixed number N of carbon atoms is considered. This and several other measures of average graphical "extension" of N-site alkanes are computed for N up to 90 (where there are over 10^35 such isomers). Fits are then made for several surmised or derived asymptotic forms, and a heuristic argument is made relating these results to geometric extensions of a random mix of (N-site) alkanes.