On the eigenvalues of weighted -Laplacian on
โ Scribed by Nawel Benouhiba
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 235 KB
- Volume
- 74
- Category
- Article
- ISSN
- 0362-546X
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๐ SIMILAR VOLUMES
We consider weighted graphs, where the edge weights are positive definite matrices. The Laplacian of the graph is defined in the usual way. We obtain an upper bound on the largest eigenvalue of the Laplacian and characterize graphs for which the bound is attained. The classical bound of Anderson and
In the note, we present an upper bound for the spectral radius of Laplacian matrix of a graph in terms of a "2-degree" of a vertex.
The importance of eigenvalue problems concerning the Laplacian is well documented in classical and modern literature. Finding the eigenvalues for various geometries of the domains has posed many challenges which include infinite systems of algebraic equations, asymptotic methods, integral equations