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The Laplacian Spectrum, Kirchhoff Index, and the Number of Spanning Trees of the Linear Heptagonal Networks

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  • Jia-Bao Liu
  • Jing Chen
  • Jing Zhao
  • Shaohui Wang
  • Ã tila Bueno

Abstract

Let Hn be the linear heptagonal networks with 2n heptagons. We study the structure properties and the eigenvalues of the linear heptagonal networks. According to the Laplacian polynomial of Hn, we utilize the method of decompositions. Thus, the Laplacian spectrum of Hn is created by eigenvalues of a pair of matrices: LA and LS of order numbers 5n+1 and 4n+1n!/r!n−r!, respectively. On the basis of the roots and coefficients of their characteristic polynomials of LA and LS, we get not only the explicit forms of Kirchhoff index but also the corresponding total number of spanning trees of Hn.

Suggested Citation

  • Jia-Bao Liu & Jing Chen & Jing Zhao & Shaohui Wang & Ã tila Bueno, 2022. "The Laplacian Spectrum, Kirchhoff Index, and the Number of Spanning Trees of the Linear Heptagonal Networks," Complexity, Hindawi, vol. 2022, pages 1-10, January.
    • Handle: RePEc:hin:complx:5584167
    DOI: 10.1155/2022/5584167
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