نتایج جستجو برای: eigenvalue of graph

تعداد نتایج: 21177063  

Journal: :Discrete Mathematics 2006
Nick C. Fiala Willem H. Haemers

In this paper, we begin the determination of all primitive strongly regular graphs with chromatic number equal to 5. Using eigenvalue techniques, we show that there are at most 43 possible parameter sets for such a graph. For each parameter set, we must decide which strongly regular graphs, if any, possessing the set are 5-chromatic. In this way, we deal completely with 34 of these parameter se...

Journal: :Discussiones Mathematicae Graph Theory 2014
Hongyan Lu Jing Luo Zhongxun Zhu

The distance spectral radius ρ(G) of a graph G is the largest eigenvalue of the distance matrix D(G). Let U (n,m) be the class of unicyclic graphs of order n with given matching number m (m 6= 3). In this paper, we determine the extremal unicyclic graph which has minimal distance spectral radius in U (n,m) \ Cn.

Journal: :J. Comb. Theory, Ser. B 2010
Jacobus H. Koolen Sejeong Bang

A non-complete geometric distance-regular graph is the point graph of a partial geometry in which the set of lines is a set of Delsarte cliques. In this paper, we prove that for fixed integer m ≥ 2, there are only finitely many non-geometric distance-regular graphs with smallest eigenvalue at least −m, diameter at least three and intersection number c2 ≥ 2.

Journal: :Journal of Graph Theory 2013
Noga Alon

A graph G is called spectrally d-degenerate if the largest eigenvalue of each subgraph of it with maximum degree D is at most √ dD. We prove that for every constant M there is a graph with minimum degree M which is spectrally 50-degenerate. This settles a problem of Dvořák and Mohar.

Journal: :Discrete Applied Mathematics 1996
Yeong-Nan Yeh Ivan Gutman Chin-Mei Fu

Graph transformations which preserve the multiplicity of the eigenvalue zero in the spectrum are known since 1970s and are of importance in chemical applications. We now show that analogous transformations hold for all graph eigenvalues that are of the form 2 cos rn, where Y is a rational number, 0 < r < 1.

Journal: :Eur. J. Comb. 2010
Yarong Wu Jinlong Shu

Let G be a simple connected graph with n vertices and n edges which we call an unicyclic graph. In this paper, we first investigate the least eigenvalue λn(G), then we present two sharp bounds of the spread s(G) of G. AMS classification: 05C50 ,05C35

Journal: :Electr. J. Comb. 2009
László Babai Barry Guiduli

Let G be a graph on n vertices with spectral radius λ (this is the largest eigenvalue of the adjacency matrix of G). We show that if G does not contain the complete bipartite graph Kt,s as a subgraph, where 2 6 t 6 s, then λ 6 (

2005
Francesc Comellas Silvia Gago

Using a simple deterministic model for the Internet graph we show that the eigenvalue power-law distribution for its adjacency matrix is a direct consequence of the degree distribution and that the graph must contain many star subgraphs. r 2005 Elsevier B.V. All rights reserved. PACS: 89.20.Hh; 89.75.Da; 89.75.Fb; 89.75.Hc

2011
Steve Kirkland Debdas Paul

For a connected graph G, we derive tight inequalities relating the smallest signless Laplacian eigenvalue to the largest normalised Laplacian eigenvalue. We investigate how vectors yielding small values of the Rayleigh quotient for the signless Laplacian matrix can be used to identify bipartite subgraphs. Our results are applied to some graphs with degree sequences approximately following a pow...

2009
Vladimir Nikiforov

We refute, improve or amplify some recent results on graph eigenvalues. In particular, we prove that if G is a graph of order n ≥ 2, maximum degree ∆, and girth at least 5, then the maximum eigenvalue μ (G) of the adjacency matrix of G satisfies μ (G) ≤ min {

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