Filters








1,157 Hits in 3.4 sec

On the kth Laplacian eigenvalues of trees with perfect matchings

Jianxi Li, Wai Chee Shiu, An Chang
2010 Linear Algebra and its Applications  
Let T + n be 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.  ... 
doi:10.1016/j.laa.2009.10.015 fatcat:eiqfrwlmzbaodemn4a4f6k7sya

The limit points of Laplacian spectra of graphs

Ji-Ming Guo
2003 Linear Algebra and its Applications  
Let G be 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.  ... 
doi:10.1016/s0024-3795(02)00508-6 fatcat:vet4cqmszrcllpdacwilg3yxme

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

Jianxi Li, Wai Chee Shiu, Wai Hong Chan
2009 Linear Algebra and its Applications  
In this paper, we provide 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.  ... 
doi:10.1016/j.laa.2008.11.016 fatcat:ksay4jroujfgjl56lo6vqp6it4

A relation between the matching number and Laplacian spectrum of a graph

Guo Ji Ming, Tan Shang Wang
2001 Linear Algebra and its Applications  
Then 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.  ... 
doi:10.1016/s0024-3795(00)00333-5 fatcat:5hktbyxiazgrrmrt7gvhq3wqo4

How can we naturally order and organize graph Laplacian eigenvectors? [article]

Naoki Saito
2018 arXiv   pre-print
This viewpoint, however, has 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.  ... 
arXiv:1801.06782v2 fatcat:gxk5m5qzefb45lsaua4s55ayim

How Can We Naturally Order and Organize Graph Laplacian Eigenvectors?

Naoki Saito
2018 2018 IEEE Statistical Signal Processing Workshop (SSP)  
This viewpoint, however, has 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.  ... 
doi:10.1109/ssp.2018.8450808 dblp:conf/ssp/Saito18 fatcat:iltrp7qkzzcwvk56dzke4tlk5u

On the structure of graph edge designs that optimize the algebraic connectivity

Yan Wan, Sandip Roy, Xu Wang, Ali Saberi, Tao Yang, Mengran Xue, Babak Malek
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).  ... 
doi:10.1109/cdc.2008.4738734 dblp:conf/cdc/WanRWSYXM08 fatcat:ha336tfm3zg3patrshhzyv6hra

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

Zhenyu Meng, Kelin Xia
2021 Science Advances  
PerSpect attributes are defined as 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.  ... 
doi:10.1126/sciadv.abc5329 pmid:33962954 pmcid:PMC8104863 fatcat:ctlqaqg6x5ewbd7mua5cu3bkze

A new upper bound for eigenvalues of the laplacian matrix of a graph

Li Jiong-Sheng, Zhang Xiao-Dong
1997 Linear Algebra and its Applications  
We first give 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  ... 
doi:10.1016/s0024-3795(96)00592-7 fatcat:q3bydoqubbgvvpgxaa56llq2hy

A Beginner's Guide to Counting Spanning Trees in a Graph [article]

Saad Quader
2012 arXiv   pre-print
(DRAFT VERSION) In this article we present 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,  ... 
arXiv:1207.7033v2 fatcat:oqootixv45gvvgwgfskgg5wzi4

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

Maryam Mirzakhah, Dariush Kiani
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 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).  ... 
doi:10.1016/j.laa.2012.05.022 fatcat:2udq6ezpsfhsbbtvmo3xvgjjm4

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

Masoumeh Farkhondeh, Mohammad Habibi, Doost Ali Mojdeh, Yongsheng Rao
2019 Mathematics  
Moreover, we characterize 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.  ... 
doi:10.3390/math7121233 fatcat:cm2u3qapnva55axm7mjzrvphlq
« Previous Showing results 1 — 15 out of 1,157 results