[Updated on Apr. 18] Integration of CiNii Articles into CiNii Research

Spectral Geometry of Graph Theory

Bibliographic Information

Other Title
  • スペクトル幾何学とグラフ理論
  • スペクトル キカガク ト グラフ リロン

Search this article


A brief survey on the spectral geometry of a finite or infinite graph is given. After the adjacency matrix, discrete Laplacian and discrete Green's formula are introduced, the spectral geometry of finite graphs, particularly, estimation of the first positive eigenvalue in terms of the Cheeger constant, examples of isospectral or cospectral graphs and the Faber=Krahn type inequality are discussed. For infinite graphs, spectrum of the discrete Laplacian, the heat kernel and Green kernel are estimated. Finally, a relation between the finite element method for the Dirichlet boundary eigenvalue problem and the eigenvalue problem of the adjacency matrix for a graph is given.


Citations (0)*help

See more


See more

Related Articles

See more

Related Data

See more

Related Books

See more

Related Dissertations

See more

Related Projects

See more

Related Products

See more


Report a problem

Back to top