  The Hosoya polynomial of a graph $G$ was introduced by H. Hosoya in 1988 as a
counting polynomial, which actually counts the number of distances of paths of
different lengths in $G$. The most interesting application of the Hosoya
polynomial is that almost all distance-based graph invariants, which are used
to predict physical, chemical and pharmacological properties of organic
molecules, can be recovered from it. In this article we give the general closed
form of the Hosoya polynomial of the generalized M\"obius ladder $M(m,n)$ for
arbitrary $m$ and for $n=3$. Moreover, we recover Wiener, hyper Wiener,
Tratch-Stankevitch-Zefirov, and Harary indices from it.
