Complexity of some special named graphs with double edges

In mathematics, one always tries to get new structures from given ones. This also applies to the realm of graphs, where one can generate many new graphs from a given set of graphs. In this paper we derive simple formulas of the complexity, number of spanning trees, of Some Special named Graphs with double edges such as Fan, Wheel and Mobius ladder, using linear algebra, Chebyshev polynomials and matrix analysis techniques.