  In this paper algebraic and combinatorial properties and a computation of the
number of the spanning trees are developed for certain graphs. To this purpose,
an original method, independent of the spectrum of the Laplacian matrix
associated to the graph, is discussed. It represents an alternative process to
compute how many and which are the spanning trees of any graph and
substantially consists in joining the spanning trees on the ground of the
number of common edges between the inner cycles of it. The algorithm and its
source code for determining the collection of all edge-sets of the spanning
trees for the class of Jahangir graphs are displayed. An application involving
such graphs in order to get a satisfactory degree of security in transmitting
confidential information is given, and finally symmetry properties of them are
highlighted.
