  In this paper we investigate the growth rate of the number of all possible
paths in graphs with respect to their length in an exact analytical way. Apart
from the typical rates of growth, i.e. exponential or polynomial, we identify
conditions for a stretched exponential type of growth. This is made possible by
combining two or more graphs over the same alphabet, in order to obtain a
discrete dynamical system generated by a triangular map, which can also be
interpreted as a discrete non-autonomous system. Since the vertices and the
edges of a graph usually are used to depict the states and transitions between
states of a discrete dynamical system, the combination of two (or more) graphs
can be interpreted as the driving, or perturbation, of one system by another.
