The Range of the Wiener Index and Its Mean Isomer Degeneracy

Abstract Sharp lower and upper bounds for the Wiener index (W) of a connected (n, m)-graph are reported; n = number of vertices, m = number of edges. The mean isomer degeneracy of W is estimated and is shown to unboundedly increase with increasing n. Thus the isomer-discriminating power of W is confirmed to be very low in the case of large molecules.