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

摘要

Let B-n 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 B-n 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 B-n are derived. Furthermore, it is interesting to find that the degree-Kirchhoff index of B-n is approximately one half of its Gutman index. (C) 2016 Elsevier Inc. All rights reserved.