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The spectra of a graph obtained from copies of a generalized Bethe tree
- Source :
-
Linear Algebra & its Applications . Jan2007, Vol. 420 Issue 2/3, p490-507. 18p. - Publication Year :
- 2007
-
Abstract
- Abstract: We generalize the concept of a Bethe tree as follows: we say that an unweighted rooted tree is a generalized Bethe tree if in each level the vertices have equal degree. If is a generalized Bethe tree of k levels then we characterize completely the eigenvalues of the adjacency matrix and Laplacian matrix of a graph obtained from the union of r copies of and the cycle connecting the r vertex roots. Moreover, we give results on the multiplicity of the eigenvalues, on the spectral radii and on the algebraic conectivity. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 420
- Issue :
- 2/3
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 23215274
- Full Text :
- https://doi.org/10.1016/j.laa.2006.08.006