Chemical applications of the Laplacian spectrum of molecular graphs: Studies of the Wiener number

The Wiener number (W) of an acyclic molecule can be expressed as a function of the Laplacian spectrum of the corresponding molecular graph. This algebraic relation enables inferences about the dependence of W on molecular structure. The graph invariants which determine the gross partsome 98% or more of W-are identified. As a consequence of this,an approximate formula for W is obtained which is capable of reproducing W of the molecular graphs of alkanes with an error of about 2%.