  The Hosoya polynomial of a graph encompasses many of its metric properties,
for instance the Wiener index (alias average distance) and the hyper-Wiener
index. An expression is obtained that reduces the computation of the Hosoya
polynomials of a graph with cut vertices to the Hosoya polynomial of the
so-called primary subgraphs. The main theorem is applied to specific
constructions including bouquets of graphs, circuits of graphs and link of
graphs. This is in turn applied to obtain the Hosoya polynomial of several
chemically relevant families of graphs. In this way numerous known results are
generalized and an approach to obtain them is simplified. Along the way several
misprints from the literature are corrected.
