  In this paper we give an exact analytical expression for the number of
spanning trees of an infinite family of outerplanar, small-world and
self-similar graphs. This number is an important graph invariant related to
different topological and dynamic properties of the graph, such as its
reliability, synchronization capability and diffusion properties. The
calculation of the number of spanning trees is a demanding and difficult task,
in particular for large graphs, and thus there is much interest in obtaining
closed expressions for relevant infinite graph families. We have also
calculated the spanning tree entropy of the graphs which we have compared with
those for graphs with the same average degree.
