نتایج جستجو برای: eigenvalue of graph
تعداد نتایج: 21177063 فیلتر نتایج به سال:
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...
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.
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.
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.
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.
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
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 (
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
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...
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 {
نمودار تعداد نتایج جستجو در هر سال
با کلیک روی نمودار نتایج را به سال انتشار فیلتر کنید