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Discrete Nodal Domain Theorems
Laplacian Eigenvectors of Graphs
Graphs with Given Degree Sequence and Maximal Spectral Radius
We describe the structure of those graphs that have largest spectral radius in the class of all connected graphs with a given degree sequence. We show that in such a graph the degree sequence is…
On the number of nodal domains of spherical harmonics
- J. Leydold
- Physics, Mathematics
- 1 April 1996
Continuous random variate generation by fast numerical inversion
This article demonstrates that with Hermite interpolation of the inverse CDF the authors can obtain very small error bounds close to machine precision, using the adaptive interval splitting method.
Automatic Nonuniform Random Variate Generation
It is shown how random variate genration algorithms work and an interface for R is suggested as an example of a statistical library, which could be used for simulation or statistical computing.
Laplacian eigenvectors of graphs : Perron-Frobenius and Faber-Krahn type theorems
Graph Laplacians.- Eigenfunctions and Nodal Domains.- Nodal Domain Theorems for Special Graph Classes.- Computational Experiments.- Faber-Krahn Type Inequalities.
Random variate generation by numerical inversion when only the density is known
The proposed algorithm is based on polynomial interpolation of the inverse CDF and Gauss-Lobatto integration and is the fastest inversion method known for generating random variates from continuous distributions when only the density function is given.
Generating generalized inverse Gaussian random variates
This paper analyzes the performance of Dagpunar’s algorithm and combines it with a new rejection method which ensures a uniformly fast generator and finds it suitable for the varying parameter case.
Minimal Cycle Bases of Outerplanar Graphs
Two-connected outerplanar graphs have a unique minimal cycle basis with length $2|E|-|V|$. They are the only Hamiltonian graphs with a cycle basis of this length.