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Number of Spanning Trees in the Sequence of Some Graphs

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  • Jia-Bao Liu
  • S. N. Daoud

Abstract

In mathematics, one always tries to get new structures from given ones. This also applies to the realm of graphs, where one can generate many new graphs from a given set of graphs. In this work, using knowledge of difference equations, we drive the explicit formulas for the number of spanning trees in the sequence of some graphs generated by a triangle by electrically equivalent transformations and rules of weighted generating function. Finally, we compare the entropy of our graphs with other studied graphs with average degree being 4, 5, and 6.

Suggested Citation

  • Jia-Bao Liu & S. N. Daoud, 2019. "Number of Spanning Trees in the Sequence of Some Graphs," Complexity, Hindawi, vol. 2019, pages 1-22, March.
    • Handle: RePEc:hin:complx:4271783
    DOI: 10.1155/2019/4271783
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    References listed on IDEAS

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    1. Liu, Jia-Bao & Pan, Xiang-Feng, 2016. "Minimizing Kirchhoff index among graphs with a given vertex bipartiteness," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 84-88.
    2. Liu, Jia-Bao & Pan, Xiang-Feng & Hu, Fu-Tao & Hu, Feng-Feng, 2015. "Asymptotic Laplacian-energy-like invariant of lattices," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 205-214.
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    Cited by:

    1. Zhang, Jingyuan & Yan, Weigen, 2020. "Counting spanning trees of a type of generalized Farey graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).

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