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Generating formulas of the number of spanning trees of some special graphs

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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.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Taibah University, 344, Al-Madinah, Saudi Arabia

    S. N. Daoud

  2. Department of Mathematics, Faculty of Science, Minufiya University, 32511, Shibin El Kom, Egypt

    S. N. Daoud

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  1. S. N. Daoud
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Correspondence to S. N. Daoud.

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Daoud, S.N. Generating formulas of the number of spanning trees of some special graphs. Eur. Phys. J. Plus 129, 146 (2014). https://doi.org/10.1140/epjp/i2014-14146-7

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  • DOI: https://doi.org/10.1140/epjp/i2014-14146-7

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