Chebyshev polynomials and spanning tree formulas for circulant and related graphs

In this paper, we extend this idea and describe how to use Chebyshev polynomials to evaluate the number of spanning trees in G when G belongs to one of three different classes of graphs: (i) when G is a circulant graph with fixed jumps (substantially simplifying earlier proofs), (ii) when G is a circulant graph with some non-fixed jumps and when (iii) G=Kn±C, where Kn is the complete graph on n vertices and C is a circulant graph.