Complexity of Some Special named Graphs and Chebyshev polynomials

Abstract

The number of spanning trees in graphs (networks) is an important invariant. Some important relations for expanding some special determinants using Chybechiev polynomials of the first kind and second kind are obtained. A large number of theorems of number of the spanning trees(its complexity), of Ladders, fans, wheels, prisms and Moebius
ladders are proved.