Advances and Applications in Discrete Mathematics
Volume 20, Issue 1, Pages 133 - 164
(January 2019) http://dx.doi.org/10.17654/ |
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THE NORMALIZED LAPLACIAN, DEGREE-KIRCHHOFF INDEX AND SPANNING TREES OF THE LINEAR LADDER-LIKE CHAINS
Ni Du and Xuechao Li
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Abstract: This paper follows up the problem posted in [11]. Let be a linear Ladder-like polyomino chain of 2n vertices with squares. In this paper, according to the decomposition theorem of normalized Laplacian polynomial, we obtain the normalized Laplacian spectrum of consists of the eigenvalues of two symmetric tridiagonal matrices of order n. Together with the relationship between the roots and coefficients of the characteristic polynomials of the above two matrices, explicit formulas for one case of the degree-Kirchhoff index and the number of spanning trees of are derived. |
Keywords and phrases: linear polyomino chain, normalized Laplacian, degree-Kirchhoff index, spanning tree.
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