  In this paper, we introduce two families of planar and self-similar graphs
which have small-world properties. The constructed models are based on an
iterative process where each step of a certain formulation of modules results
in a final graph with a self-similar structure. The number of spanning trees of
a graph is one of the most graph-theoretical parameters, where its applications
range from the theory of networks to theoretical chemistry. Two explicit
formulas are introduced for the number of spanning trees for the two models.
With explicit formulas for some of their topological parameters as well.
