Further Applications of Chebyshev Polynomials in the Derivation of Spanning Tree Formulas for Circulant Graphs

  • Yuanping Zhang
  • Mordecai J. Golin
Conference paper
Part of the Trends in Mathematics book series (TM)


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. Boesch and Prodinger [6] have shown how to use Chebyshev polynomials to evaluate the associated determinants and derive closed formulas for the number of spanning trees of graphs in certain special classes.

In this paper we extend this work to describe two further applications of Chebyshev polynomials in the evaluation of the numbers of spanning trees of Circulant Graphs.


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Copyright information

© Springer Basel AG 2002

Authors and Affiliations

  • Yuanping Zhang
    • 1
    • 2
  • Mordecai J. Golin
    • 1
  1. 1.Department of Computer ScienceHong Kong U.S.T. Clear Water Bay KowloonHong Kong
  2. 2.The Department of MathematicsHunan Normal UniversityChangshaPRC

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