scholarly journals Comparison of Steklov eigenvalues and Laplacian eigenvalues on graphs

2021 ◽  
Author(s):  
Yongjie Shi ◽  
Chengjie Yu
Keyword(s):  
Laplacian Eigenvalues ◽  
Steklov Eigenvalues

On the Laplacian Eigenvalues of Gn,p

2007 ◽  
Vol 16 (6) ◽  
pp. 923-946 ◽  
Author(s):  
AMIN COJA-OGHLAN
Keyword(s):  
Random Graphs ◽  
Spectral Gap ◽  
Degree Sequences ◽  
Laplacian Eigenvalues ◽  
Combinatorial Laplacian ◽  
Laplacian Spectra

We investigate the Laplacian eigenvalues of sparse random graphs Gnp. We show that in the case that the expected degree d = (n-1)p is bounded, the spectral gap of the normalized Laplacian $\LL(\gnp)$ is o(1). Nonetheless, w.h.p. G = Gnp has a large subgraph core(G) such that the spectral gap of $\LL(\core(G))$ is as large as 1-O (d−1/2). We derive similar results regarding the spectrum of the combinatorial Laplacian L(Gnp). The present paper complements the work of Chung, Lu and Vu [8] on the Laplacian spectra of random graphs with given expected degree sequences. Applied to Gnp, their results imply that in the ‘dense’ case d ≥ ln2n the spectral gap of $\LL(\gnp)$ is 1-O (d−1/2) w.h.p.

scholarly journals On the sum of the Laplacian eigenvalues of a tree

2011 ◽  
Vol 435 (2) ◽  
pp. 371-399 ◽  
Author(s):  
Eliseu Fritscher ◽  
Carlos Hoppen ◽  
Israel Rocha ◽  
Vilmar Trevisan
Keyword(s):  
Laplacian Eigenvalues

scholarly journals On the sum of signless Laplacian eigenvalues of a graph

2013 ◽  
Vol 438 (11) ◽  
pp. 4539-4546 ◽  
Author(s):  
F. Ashraf ◽  
G.R. Omidi ◽  
B. Tayfeh-Rezaie
Keyword(s):  
Laplacian Eigenvalues ◽  
Signless Laplacian
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