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

Regular Article

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.

Keywords

Span Tree Connected Graph Travel Salesman Problem Regular Graph Chebyshev Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceTaibah UniversityAl-MadinahSaudi Arabia
  2. 2.Department of Mathematics, Faculty of ScienceMinufiya UniversityShibin El KomEgypt

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