A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
On the kth Laplacian eigenvalues of trees with perfect matchings

2010
*
Linear Algebra and its Applications
*

Let T + n be

doi:10.1016/j.laa.2009.10.015
fatcat:eiqfrwlmzbaodemn4a4f6k7sya
*the*set*of*all*trees**of*order n with perfect matchings. ... In this paper, we prove that for any*tree*T ∈ T + n , its*kth*largest*Laplacian**eigenvalue*μ k (T) satisfies μ k (T) = 2 when n = 2k, and when n / = 2k. ... Acknowledgments*The*authors would like to thank*the*referees for their careful reading, valuable suggestions and useful comments. ...##
###
The limit points of Laplacian spectra of graphs

2003
*
Linear Algebra and its Applications
*

Let G be

doi:10.1016/s0024-3795(02)00508-6
fatcat:vet4cqmszrcllpdacwilg3yxme
*a*graph on n vertices. Denote by L(G)*the**Laplacian*matrix*of*G. ... This observation let Fiedler to call α(G)*the*algebraic connectivity*of**the*graph G. In this paper,*the*limit points*of**Laplacian*spectra*of*graphs are investigated. ... Acknowledgements*The*author would like to thank Prof. Y. ...##
###
Page 4631 of Mathematical Reviews Vol. , Issue 2000g
[page]

2000
*
Mathematical Reviews
*

We show that every

*Laplacian*limit point*of**the**kth*largest (or smallest)*Laplacian**of**a*graph is*a*limit point*of**the*(Kk + 1)st largest (or smallest)*Laplacian**eigenvalue*. ...*The*matrix L(G) = D(G)—*A*(G) is called*the**Laplacian*matrix, and its*eigenvalues*are called*the**Laplacian**eigenvalues**of*G. In this paper, we define limit points*of**the**Laplacian**eigenvalues*. ...##
###
Some results on the Laplacian eigenvalues of unicyclic graphs

2009
*
Linear Algebra and its Applications
*

In this paper, we provide

doi:10.1016/j.laa.2008.11.016
fatcat:ksay4jroujfgjl56lo6vqp6it4
*the*smallest value*of**the*second largest*Laplacian**eigenvalue*for any unicyclic graph, and find*the*unicyclic graphs attaining that value. ... And also give an "asymptotically good" upper bounds for*the*second largest*Laplacian**eigenvalues**of*unicyclic graphs. ... We also wish to thank*the*referee for giving several valuable comments and suggestions. ...##
###
A relation between the matching number and Laplacian spectrum of a graph

2001
*
Linear Algebra and its Applications
*

Then

doi:10.1016/s0024-3795(00)00333-5
fatcat:5hktbyxiazgrrmrt7gvhq3wqo4
*the*number*of*edges in M(G) is*a*lower bound for*the*number*of**Laplacian**eigenvalues**of*G exceeding 2. ... Let G be*a*graph, its*Laplacian*matrix is*the*difference*of**the*diagonal matrix*of*its vertex degrees and its adjacency matrix. In this paper, we generalize*a*result in (R. Merris, Port. ... Acknowledgement*The*authors express their thanks to*the*referee for some helpful suggestions. ...##
###
How can we naturally order and organize graph Laplacian eigenvectors?
[article]

2018
*
arXiv
*
pre-print

This viewpoint, however, has

arXiv:1801.06782v2
fatcat:gxk5m5qzefb45lsaua4s55ayim
*a*fundamental flaw: on*a*general graph,*the**Laplacian**eigenvalues*cannot be interpreted as*the*frequencies*of**the*corresponding eigenvectors. ... We demonstrate its effectiveness using*a*synthetic graph as well as*a*dendritic*tree**of**a*retinal ganglion cell*of**a*mouse. ... Fig. 5 . 5 Embedding*of**the**Laplacian*eigenvectors*of**the*RGC*tree*into R 3 using Algorithm 4.1 with α = 0.5. instead*of*Fig. 1. Then*a*natu-Fig. 2. ...##
###
How Can We Naturally Order and Organize Graph Laplacian Eigenvectors?

2018
*
2018 IEEE Statistical Signal Processing Workshop (SSP)
*

This viewpoint, however, has

doi:10.1109/ssp.2018.8450808
dblp:conf/ssp/Saito18
fatcat:iltrp7qkzzcwvk56dzke4tlk5u
*a*fundamental flaw: on*a*general graph,*the**Laplacian**eigenvalues*cannot be interpreted as*the*frequencies*of**the*corresponding eigenvectors. ... We demonstrate its effectiveness using*a*synthetic graph as well as*a*dendritic*tree**of**a*retinal ganglion cell*of**a*mouse. ... Fig. 5 . 5 Embedding*of**the**Laplacian*eigenvectors*of**the*RGC*tree*into R 3 using Algorithm 4.1 with α = 0.5. instead*of*Fig. 1. Then*a*natu-Fig. 2. ...##
###
On the structure of graph edge designs that optimize the algebraic connectivity

2008
*
2008 47th IEEE Conference on Decision and Control
*

*the*design upon addition

*of*

*a*new vertex. ... Using these characterizations, we obtain an alternative finite-search algorithm for finding

*the*optimal design in

*tree*graphs that is quadratic in

*the*number

*of*vertices, and further address update

*of*... (i.e.,

*the*second-smallest

*eigenvalue*

*of*

*the*

*Laplacian*matrix associated with

*the*graph). ...

##
###
Persistent spectral–based machine learning (PerSpect ML) for protein-ligand binding affinity prediction

2021
*
Science Advances
*

PerSpect attributes are defined as

doi:10.1126/sciadv.abc5329
pmid:33962954
pmcid:PMC8104863
fatcat:ctlqaqg6x5ewbd7mua5cu3bkze
*the*function*of*spectral variables over*the*filtration value. ... Different from all previous spectral models,*a*filtration process is introduced to generate*a*sequence*of*spectral models at various different scales. ... Author contributions: K.X. conceived and designed*the*study. Z.M. and K.X. performed*the*calculation. K.X. contributed to*the*preparation*of**the*manuscript. ...##
###
A new upper bound for eigenvalues of the laplacian matrix of a graph

1997
*
Linear Algebra and its Applications
*

We first give

doi:10.1016/s0024-3795(96)00592-7
fatcat:q3bydoqubbgvvpgxaa56llq2hy
*a*result on*eigenvalues**of**the*line graph*of**a*graph. We then use*the*result to present*a*new upper bound for*eigenvalues**of**the**Laplacian*matrix*of**a*graph. ... Moreover we determine all graphs*the*largest*eigenvalue**of*whose*Laplacian*matrix reaches*the*upper bound. ...*The**Laplacian*matrix*of**a*graph, which dates back to Kirchhoffs theorem [5] , plays an important role in*the*study*of*spanning*trees*, spectra, isomorphisms,*the*connectivity*of**a*graph, and biological ...##
###
A Beginner's Guide to Counting Spanning Trees in a Graph
[article]

2012
*
arXiv
*
pre-print

(DRAFT VERSION) In this article we present

arXiv:1207.7033v2
fatcat:oqootixv45gvvgwgfskgg5wzi4
*a*proof*of**the*famous Kirchoff's Matrix-*Tree*theorem, which relates*the*number*of*spanning*trees*in*a*connected graph with*the*cofactors (and*eigenvalues*)*of*... For example, we prove*the*elementary properties*of*determinants, relationship between*the*roots*of*characteristic polynomial (that is,*eigenvalues*) and*the*minors,*the*Cauchy-Binet formula,*the*Laplace ... Since*the*incidence matrix is linked to*the*combinatorial*Laplacian*matrix*of**the*graph,*the*number*of*spanning*trees*in*of**the*graph is linked to*the**eigenvalues**of**the*combinatorial*Laplacian*matrix, ...##
###
Page 1796 of Mathematical Reviews Vol. , Issue 92d
[page]

1992
*
Mathematical Reviews
*

Summary: “Let

*A*, be*the**kth*largest*eigenvalue**of**a**tree*T (or*a*forest F) with n vertices, i.e.,*A*; > Az >--- > An; then Ay = —Apn_x41, and*A*, is*the*smallest positive*eigenvalue*, where q is*the*edge ... > 1) positive*eigenvalue**of**a*forest is 2 cos[kz/(2k + 1)]; (d)*the*sharp lower bound*of**the**kth*(k = 2,3,4,5) positive*eigenvalue**of**a**tree*is 2cos6,, where 6, is*the*unique solution to sin(2k + 1)@ — ...##
###
Some results on signless Laplacian coefficients of graphs

2012
*
Linear Algebra and its Applications
*

Let Q G (x) = det(xI − Q (G)) = n i=0 (−1) i ζ i x n−i be

doi:10.1016/j.laa.2012.05.022
fatcat:2udq6ezpsfhsbbtvmo3xvgjjm4
*the*characteristic polynomial*of**the*signless*Laplacian*matrix*of**a*graph G. ... Due to*the*nice properties*of**the*signless*Laplacian*matrix, Q (G), in comparison with*the*other matrices related to graphs, ζ -ordering, an ordering based on*the*coefficients*of**the*signless*Laplacian*... Acknowledgments*The*research*of**the*second author was in part supported by*a*grant from*the*Institute for Research in Fundamental Sciences (IPM) (Grant No. 90050115). ...##
###
Page 1796 of Mathematical Reviews Vol. , Issue 92c
[page]

1992
*
Mathematical Reviews
*

Summary: “Let

*A*; be*the**kth*largest*eigenvalue**of**a**tree*T (or*a*forest F’) with n vertices, i.e.,*A*; > Az >--- > An; then Ay = —An_ x41, and*A*, is*the*smallest positive*eigenvalue*, where q is*the*edge ... > 1) positive*eigenvalue**of**a*forest is 2 cos[kz/(2k + 1)]; (d)*the*sharp lower bound*of**the**kth*(k = 2, 3,4, 5) positive*eigenvalue**of**a**tree*is 2cos6,, where 6; is*the*unique solution to sin(2k + 1) ...##
###
Some Bicyclic Graphs Having 2 as Their Laplacian Eigenvalues

2019
*
Mathematics
*

Moreover, we characterize

doi:10.3390/math7121233
fatcat:cm2u3qapnva55axm7mjzrvphlq
*the*broken sun graphs and*the*one-edge connection*of*two broken sun graphs by their*Laplacian**eigenvalue*2. ... We also provide*a*condition under which*a*bicyclic graph with*a*perfect matching has*a**Laplacian**eigenvalue*2. ... Acknowledgments: We would like to thank*the*anonymous referees for their valuable suggestions and comments. Conflicts*of*Interest:*The*authors declare no conflict*of*interest. ...
« Previous

*Showing results 1 — 15 out of 1,157 results*