Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Kirchhoff 's Matrix Tree Theorem permits the calculation of the number of spanning trees in any given graph G through the evaluation of the determinant of an associated matrix. In the case of some special graphs Boesch and Prodinger [Graph Combin. 2 (1986) 191-200] have shown how to use properties of Chebyshev polynomials to evaluate the associated determinants and derive closed formulas for the number of spanning trees of graphs. ,  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=K"n+/-C, where K"n is the complete graph on n vertices and C is a circulant graph.
['Yuanping Zhang', 'Xuerong Yong', 'Mordecai J. Golin']
I am writing a research paper on a idea Chebyshev polynomials and spanning tree formulas for circulant and related graphs
[{"from": "human", "value": "I am writing a research paper on a idea Chebyshev polynomials and spanning tree formulas for circulant and related graphs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Kirchhoff 's Matrix Tree Theorem permits the calculation of the number of spanning trees in any given graph G through the evaluation of the determinant of an associated matrix. In the case of some special graphs Boesch and Prodinger [Graph Combin. 2 (1986) 191-200] have shown how to use properties of Chebyshev polynomials to evaluate the associated determinants and derive closed formulas for the number of spanning trees of graphs. ,  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=K\"n+/-C, where K\"n is the complete graph on n vertices and C is a circulant graph."}]