Abstract
Boesh and Prodinger (J. Graphs Comb. 2, 191 (1986)) illustrated how to use the properties of Chebyshev polynomials to calculate the associated determinants and derived closed formula for the number of spanning trees of graphs. In this paper, we extend this idea and describe how to use Chebyshev polynomials to calculate the number of spanning trees (the complexity) in a graph G, when G belongs to one of the following different classes of graphs: i) Grid graph; ii) torus graph; iii) cylinder graph; iv) lattice graph; v) hypercube graph; and vi) stacked book graph.