Abstract
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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Zhang, Y., Golin, M.J. (2002). Further Applications of Chebyshev Polynomials in the Derivation of Spanning Tree Formulas for Circulant Graphs. In: Chauvin, B., Flajolet, P., Gardy, D., Mokkadem, A. (eds) Mathematics and Computer Science II. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8211-8_34
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DOI: https://doi.org/10.1007/978-3-0348-8211-8_34
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