The normalized Laplacian, degree-Kirchhoff index and spanning trees of the linear polyomino chains

Jing Huang, Shuchao Li and Xuechao Li

Applied Mathematics and Computation, 2016, vol. 289, issue C, 324-334

Abstract: Let Bn be a linear polyomino chain with n squares. In this paper, according to the decomposition theorem of normalized Laplacian polynomial, we obtain that the normalized Laplacian spectrum of Bn consists of the eigenvalues of two symmetric tridiagonal matrices of order n+1. Together with the relationship between the roots and coefficients of the characteristic polynomials of the above two matrices, explicit closed formulas of the degree-Kirchhoff index and the number of spanning trees of Bn are derived. Furthermore, it is interesting to find that the degree-Kirchhoff index of Bn is approximately one half of its Gutman index.

Keywords: Linear polyomino chain; Normalized Laplacian; Degree-Kirchhoff index; Spanning tree (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (12)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:289:y:2016:i:c:p:324-334

DOI: 10.1016/j.amc.2016.05.024

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