On graphs whose Laplacian matrices have distinct integer eigenvalues

2005 ◽  
Vol 50 (2) ◽  
pp. 162-174 ◽  
Author(s):  
Shaun M. Fallat ◽  
Stephen J. Kirkland ◽  
Jason J. Molitierno ◽  
M. Neumann
Keyword(s):  
Laplacian Matrices ◽  
Distinct Integer

scholarly journals The Laplacian Energy of Conjugacy Class Graph of Some Finite Groups

MATEMATIKA ◽  
2019 ◽  
Vol 35 (1) ◽  
pp. 59-65
Author(s):  
Rabiha Mahmoud ◽  
Amira Fadina Ahmad Fadzil ◽  
Nor Haniza Sarmin ◽  
Ahmad Erfanian
Keyword(s):  
Conjugacy Class ◽  
Finite Groups ◽  
Dihedral Group ◽  
Dihedral Groups ◽  
Laplacian Eigenvalues ◽  
Laplacian Matrices ◽  
Laplacian Energy ◽  
The Difference ◽  
Generalized Quaternion ◽  
Class Graph

Let G be a dihedral group and its conjugacy class graph. The Laplacian energy of the graph, is defined as the sum of the absolute values of the difference between the Laplacian eigenvalues and the ratio of twice the edges number divided by the vertices number. In this research, the Laplacian matrices of the conjugacy class graph of some dihedral groups, generalized quaternion groups, quasidihedral groups and their eigenvalues are first computed. Then, the Laplacian energy of the graphs are determined.

scholarly journals Spectra of Laplacian Matrices of Weighted Graphs: Structural Genericity Properties

2018 ◽  
Vol 78 (1) ◽  
pp. 372-394 ◽  
Author(s):  
Camille Poignard ◽  
Tiago Pereira ◽  
Jan Philipp Pade
Keyword(s):  
Weighted Graphs ◽  
Laplacian Matrices

scholarly journals Random walks with long-range steps generated by functions of Laplacian matrices

2018 ◽  
Vol 2018 (4) ◽  
pp. 043404 ◽  
Author(s):  
A P Riascos ◽  
T M Michelitsch ◽  
B A Collet ◽  
A F Nowakowski ◽  
F C G A Nicolleau
Keyword(s):  
Random Walks ◽  
Long Range ◽  
Laplacian Matrices

scholarly journals Distances in Weighted Trees and Group Inverse of Laplacian Matrices

1997 ◽  
Vol 18 (4) ◽  
pp. 827-841 ◽  
Author(s):  
Stephen J. Kirkland ◽  
Michael Neumann ◽  
Bryan L. Shader
Keyword(s):  
Group Inverse ◽  
Laplacian Matrices ◽  
Weighted Trees

scholarly journals On the spectra of nonsymmetric Laplacian matrices

2005 ◽  
Vol 399 ◽  
pp. 157-168 ◽  
Author(s):  
Rafig Agaev ◽  
Pavel Chebotarev
Keyword(s):  
Laplacian Matrices

scholarly journals EMPIRICAL DISTRIBUTIONS OF LAPLACIAN MATRICES OF LARGE DILUTE RANDOM GRAPHS

2012 ◽  
Vol 01 (03) ◽  
pp. 1250004 ◽  
Author(s):  
TIEFENG JIANG
Keyword(s):  
Random Graph ◽  
Random Graphs ◽  
Spectral Properties ◽  
Empirical Distribution ◽  
Laplacian Matrix ◽  
Free Convolution ◽  
Laplacian Matrices ◽  
Empirical Distributions ◽  
Large N ◽  
Eigenvalues Of The Laplacian

We study the spectral properties of the Laplacian matrices and the normalized Laplacian matrices of the Erdös–Rényi random graph G(n, pn) for large n. Although the graph is simple, we discover some interesting behaviors of the two Laplacian matrices. In fact, under the dilute case, that is, pn ∈ (0, 1) and npn → ∞, we prove that the empirical distribution of the eigenvalues of the Laplacian matrix converges to a deterministic distribution, which is the free convolution of the semi-circle law and N(0, 1). However, for its normalized version, we prove that the empirical distribution converges to the semi-circle law.

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