I. Gutman et G. Domotor, WIENER NUMBER OF POLYPHENYLS AND PHENYLENES, Zeitschrift fur Naturforschung. A, A journal of physical sciences, 49(11), 1994, pp. 1040-1044
It is shown that the values which the Wiener numbers of isomeric polyp
henyls may assume are all congruent module 36. Similarly, the Wiener n
umbers of isomeric phenylens are always congruent module 18. These fin
dings provide a rationalization for the known fact that the isomer-dis
criminating power of the Wiener number is rather weak. Extensions of t
he present results to more general classes of graphs are also pointed
out.