Laplace eigenvalues of graphs—a survey
نویسندگان
چکیده
منابع مشابه
Some Applications of Laplace Eigenvalues of Graphs Some Applications of Laplace Eigenvalues of Graphs
In the last decade important relations between Laplace eigenvalues and eigenvectors of graphs and several other graph parameters were discovered. In these notes we present some of these results and discuss their consequences. Attention is given to the partition and the isoperimetric properties of graphs, the max-cut problem and its relation to semideenite programming, rapid mixing of Markov cha...
متن کاملSome Applications of Laplace Eigenvalues of Graphs∗
In the last decade important relations between Laplace eigenvalues and eigenvectors of graphs and several other graph parameters were discovered. In these notes we present some of these results and discuss their consequences. Attention is given to the partition and the isoperimetric properties of graphs, the max-cut problem and its relation to semidefinite programming, rapid mixing of Markov ch...
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We describe a highly efficient numerical scheme for finding two-sided bounds for the eigenvalues of the fractional Laplace operator (−∆)α/2 in the unit ball D ⊂ Rd, with a Dirichlet condition in the complement of D. The standard Rayleigh–Ritz variational method is used for the upper bounds, while the lower bounds involve the less-known Aronszajn method of intermediate problems. Both require exp...
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To every compact Riemannian manifold M there corresponds the sequence 0 = X1 < X2 < X3 .< ... of eigenvalues for the Laplace operator on M. It is not known just how much information about M can be extracted from this sequence.' This note will show that the sequence does not characterize M completely, by exhibiting two 16-dimensional toruses which are distinct as Riemannian manifolds but have th...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1992
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)90288-q