The Context: Classical, Laplacian, and Normalized Laplacian eigenvalues of a set of trees available at [1] have been computed using high-performance Linear Algebra software LAPACK (C version)(that is, the f2c'd version) [2,3,4]. Important parameters are n, the number of vertices and d , the diameter, where 4 ≤ n ≤ 18 . This script allows the user to select a subset of interest, for which data obtained from the distribution of the corresponding classical/laplacian eigenvalues is displayed.
References:
[1] From the webpage of Brendan McKay: http://cs.anu.edu.au/~bdm/data/trees.html
[2] Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, D. Sorensen, Lapack User Guide , Third Edition, SIAM 1999.
[3] http://en.wikipedia.org/wiki/LAPACK
[4] http://www.netlib.org/lapack

Please choose the number of vertices n and the diameter d : n = 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 , d : 2 ≤ d ≤ n-1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
operation: list eigenvalues and energy list distribution stats show adj. matrices
type: classical laplacian normalized laplacian
order by: energy smallest eig second smallest eig

JBC, 23/12/2009, last modified 30/10/2013, 01/07/2020