45,346 research outputs found
The non-bipartite integral graphs with spectral radius three
In this paper, we classify the connected non-bipartite integral graphs with
spectral radius three.Comment: 18 pages, 5 figures, 2 table
Connected Hypergraphs with Small Spectral Radius
In 1970 Smith classified all connected graphs with the spectral radius at
most . Here the spectral radius of a graph is the largest eigenvalue of its
adjacency matrix. Recently, the definition of spectral radius has been extended
to -uniform hypergraphs. In this paper, we generalize the Smith's theorem to
-uniform hypergraphs. We show that the smallest limit point of the spectral
radii of connected -uniform hypergraphs is . We
discovered a novel method for computing the spectral radius of hypergraphs, and
classified all connected -uniform hypergraphs with spectral radius at most
.Comment: 20 pages, fixed a missing class in theorem 2 and other small typo
Efficient algorithms for deciding the type of growth of products of integer matrices
For a given finite set of matrices with nonnegative integer entries
we study the growth of We show how to determine in polynomial time whether the growth with
is bounded, polynomial, or exponential, and we characterize precisely all
possible behaviors.Comment: 20 pages, 4 figures, submitted to LA
Multigrid Waveform Relaxation on Spatial Finite Element Meshes: The Discrete-Time Case
The efficiency of numerically solving time-dependent partial differential equations on parallel computers can be greatly improved by computing the solution on many time levels simultaneously. The theoretical properties of one such method, namely the discrete-time multigrid waveform relaxation method, are investigated for systems of ordinary differential equations obtained by spatial finite-element discretisation of linear parabolic initial-boundary value problems. The results are compared to the corresponding continuous-time results. The theory is illustrated for a one-dimensional and a two-dimensional model problem and checked against results obtained by numerical experiments
On the positive and negative inertia of weighted graphs
The number of the positive, negative and zero eigenvalues in the spectrum of
the (edge)-weighted graph are called positive inertia index, negative
inertia index and nullity of the weighted graph , and denoted by ,
, , respectively. In this paper, the positive and negative
inertia index of weighted trees, weighted unicyclic graphs and weighted
bicyclic graphs are discussed, the methods of calculating them are obtained.Comment: 12. arXiv admin note: text overlap with arXiv:1107.0400 by other
author
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