A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Filters
Bounds of eigenvalues of graphs
1993
Discrete Mathematics
Preserved Fulltext
We get some bounds of the eigenvalues of graphs and propose a few open problems. ...
The eigenvalues of a graph are the eigenvalues of its adjacency matrix. This paper presents an algebraically defined invariant system of a graph. ...
,-Jab Bounds qf eigenvalues Of graphs 2. The spectral radius of graphs 67 The largest eigenvalue A,(G) is often called the spectral radius of G. ...
doi:10.1016/0012-365x(93)90007-g
fatcat:im44remynfbvhig3z7abym2gvm
Bounds on Geometric Eigenvalues of Graphs
[article]
2015
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Other Versions
The smallest nonzero eigenvalue of the normalized Laplacian matrix of a graph has been extensively studied and shown to have many connections to properties of the graph. ...
We consider general bounds on λ(G, X) and λ(G, H), where H is a graph under the standard distance metric, generalizing some existing results for the standard eigenvalue. ...
Introduction The use of eigenvalues to study graphs has a long history in graph theory. ...
arXiv:1501.03436v3
fatcat:i7ntostamrbfvnlwr3hio6pkhe
Conjectured bound for the distribution of eigenvalues of a graph
[article]
2019
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Note that this fulltext copy is not of the "primary" version of this work. The version it corresponds to is:
2018 pre-print arXiv:1709.04009v3 fatcat:qvbwreqo65d4nmu4qvdfyr47e4Other Versions
We consider the relationship between this bound and the number of eigenvalues that lie within the interval -1 to 0, which we denote n_(-1,0)(G). ...
We conjecture that for any graph n^-(G) + n^-(G̅) < 1.5(n - 1), and prove this bound for various classes of graphs and for almost all graphs. ...
Acknowledgement We would like to thank Josh Tobin for very helpful comments and suggestions on this paper, in particular in regard to random graphs. ...
arXiv:1709.04009v4
fatcat:y3wt3jdb2jbczccxc44lmctp4u
Bounds of Eigenvalues of -Minor Free Graphs
2009
Journal of Inequalities and Applications
Preserved Fulltext
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.
The spectral radius ρ G of a graph G is the largest eigenvalue of its adjacency matrix. Let λ G be the smallest eigenvalue of G. ...
In this paper, we have described the K 3,3 -minor free graphs and showed that A let G be a simple graph with order n ≥ 7. If G has no K 3,3 -minor, then ρ G ≤ 1 √ 3n − 8. ...
Work supported by NNSF of China no. 10671074 and NSF of Zhejian Province no. Y7080364 . ...
doi:10.1155/2009/852406
fatcat:ebikld2ldrantbzu5hahp63oea
Lower bounds of the Laplacian graph eigenvalues
2004
Indagationes mathematicae
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
In this paper we prove that all positive eigenvalues of the Laplacian of an arbitrary simple graph have some positive lower bounds. ...
For a fixed integer k ~> 1 we call a graph without isolated vertices k-minimal if its kth greatest Laplacian eigenvalue reaches this lower bound, We describe all 1-minimal and 2-minimal graphs and we prove ...
Next for fixed i = 1,2 ..... n he considered the minimal values of/z i (G) in the class of all connected graphs with n vertices. So, for instance, its #3 (G) = )~n-2(G) in our notations. ...
doi:10.1016/s0019-3577(04)80021-1
fatcat:g6vxheb76nhjtevmxkp6pla5hy
Bounds on normalized Laplacian eigenvalues of graphs
2014
Journal of Inequalities and Applications
Preserved Fulltext
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.
Let G be a simple connected graph of order n, where n ≥ 2. Its normalized Laplacian eigenvalues are 0 = λ 1 ≤ λ 2 ≤ · · · ≤ λ n ≤ 2. ...
In this paper, some new upper and lower bounds on λ n are obtained, respectively. Moreover, connected graphs with λ 2 = 1 (or λ n-1 = 1) are also characterized. MSC: 05C50; 15A48 ...
This work was supported by NSF of China ...
doi:10.1186/1029-242x-2014-316
fatcat:ngdstu6uzbdbval22lqxretjq4
Upper bounds for Steklov eigenvalues of subgraphs of polynomial growth Cayley graphs
[article]
2021
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is application/pdf.
Other Versions
We study the Steklov problem on a subgraph with boundary (Ω,B) of a polynomial growth Cayley graph Γ. ...
We prove that for each k ∈ℕ, the k^ eigenvalue tends to 0 proportionally to 1/|B|^1/d-1, where d represents the growth rate of Γ. ...
I also wish to thank Niel Smith and Antoine Gagnebin for their careful proofreading of this paper and for their various remarks which have led to its improvement. ...
arXiv:2101.04402v1
fatcat:4iepelp5wnf4hpj66nzhgvan7a
Eigenvalue bounds for some classes of matrices associated with graphs
[article]
2020
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
Using these bounds, first we derive bounds for the second largest and smallest eigenvalues of adjacency matrices of k-regular graphs. ...
Then, we establish some bounds for the second largest and the smallest eigenvalues of the normalized adjacency matrices of graphs and the second smallest eigenvalue and the largest eigenvalue of the Laplacian ...
Eigenvalue bounds for Laplacian matrix In this section, we establish bounds for eigenvalues of Laplacian matrices of connected graphs. ...
arXiv:1812.04916v2
fatcat:dyecq5nborcijhzb7vezbu6nbi
A family of diameter-based eigenvalue bounds for quantum graphs
[article]
2019
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
We establish a sharp lower bound on the first non-trivial eigenvalue of the Laplacian on a metric graph equipped with natural (i.e., continuity and Kirchhoff) vertex conditions in terms of the diameter ...
We also give a family of corresponding lower bounds for the higher eigenvalues under the assumption that the total length of the graph is sufficiently large compared with its diameter. ...
of the eigenvalues (1.1), for example in terms of the total length, diameter, number of edges or vertices, edge connectivity,. . . of the graph, or establishing properties of extremising graphs realising ...
arXiv:1807.08185v2
fatcat:ikzbsoebjba3zos2dffv6s4nri
On a Lower Bound for the Laplacian Eigenvalues of a Graph
2017
Graphs and Combinatorics
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Note that this fulltext copy is not of the "primary" version of this work. The version it corresponds to is:
2017 pre-print arXiv:1707.03221v1 fatcat:q4h55nwb2nan3nvcjeqh2qdxueOther Versions
If μ_m and d_m denote, respectively, the m-th largest Laplacian eigenvalue and the m-th largest vertex degree of a graph, then μ_m ≥ d_m-m+2. ...
In this paper we consider the problem of characterising graphs satisfying μ_m = d_m-m+2. In particular we give a full classification of graphs with μ_m = d_m-m+2 ≤ 1. ...
When it is clear which graph is under consideration, we merely write d i and µ i . Brouwer and Haemers [1, Theorem 1] proved the following lower bound for the mth largest Laplacian eigenvalue of Γ. ...
doi:10.1007/s00373-017-1835-y
fatcat:3ptb43oh3bhlhnp5qswggihvde
A majorization bound for the eigenvalues of some graph Laplacians
[article]
2004
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
It is conjectured that the Laplacian spectrum of a graph is majorized by its conjugate degree sequence. In this paper, we prove that this majorization holds for a class of graphs including trees. ...
We also show that a generalization of this conjecture to graphs with Dirichlet boundary conditions is equivalent to the original conjecture. ...
Bounds on λ n−1 (L(G)) then give information on how well connected a graph is, and are useful, for example, in showing the existence of expander graphs. ...
arXiv:math/0411153v1
fatcat:m52hmi7fsjbtnpee6glr3p6cym
Upper bound for the Laplacian eigenvalues of a graph
[article]
2011
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
In this note we give a new upper bound for the Laplacian eigenvalues of an unweighted graph. Let G be a simple graph on n vertices. ...
We also introduce upper and lower bound for the Laplacian eigenvalues of weighted graphs, and compare it with the special case of unweighted graphs. ...
We are ready now to present the upper bound for the Laplacian eigenvalues of weighted graphs: Theorem 4. Let G be a simple weighted graph, and let a be the maximal weight of an edge in G. ...
arXiv:1106.0769v1
fatcat:yoeplvq7rfcd7cv2fgfapja2wa
An upper bound for higher order eigenvalues of symmetric graphs
[article]
2020
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
In this paper, we derive an upper bound for higher order eigenvalues of the normalized Laplace operator associated with a symmetric finite graph in terms of lower order eigenvalues. ...
We recall some basic facts on the theory of eigenvalues of a regular graph. Let G = (V, E) be a d-regular graph, d ≥ 1, and put N := #V . ...
Let G be a symmetric graph. Let λ be an eigenvalue of ∆ and let {u α } m α=1 be an orthonormal basis of W λ . ...
arXiv:2006.07632v1
fatcat:dk2lo7w64vdwtp2wkmuwmjja44
An Interlacing Approach for Bounding the Sum of Laplacian Eigenvalues of Graphs
[article]
2013
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
We apply eigenvalue interlacing techniques for obtaining lower and upper bounds for the sums of Laplacian eigenvalues of graphs, and characterize equality. ...
As a consequence we obtain inequalities involving bounds for some well-known parameters of a graph, such as edge-connectivity, and the isoperimetric number. ...
. ✷ Both bounds are tight for the complete graph K n . ...
arXiv:1307.4670v2
fatcat:cg3h6ai77babdfyojsfpzadsg4
Sharp bounds on the least eigenvalue of a graph determined from edge clique partitions
[article]
2022
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
Other Versions
Sharp bounds on the least eigenvalue of an arbitrary graph are presented. ...
As an application, we prove that the least eigenvalue of the n-Queens' graph 𝒬(n) is equal to -4 for every n ≥ 4 and it is also proven that the multiplicity of this eigenvalue is (n-3)^2. ...
I.S.C. also thanks the support of FCT via PhD Scholarship PD/BD/150538/2019. ...
arXiv:2201.01224v4
fatcat:v5liloux7rhxtptodmg5qgwfv4
« Previous
Showing results 1 — 15 out of 130,307 results