Back to Search Start Over

Spectra of generalized Bethe trees attached to a path

Authors :
Rojo, Oscar
Medina, Luis
Source :
Linear Algebra & its Applications. Jan2009, Vol. 430 Issue 1, p483-503. 21p.
Publication Year :
2009

Abstract

Abstract: A generalized Bethe tree is a rooted tree in which vertices at the same distance from the root have the same degree. Let be a path of m vertices. Let be a set of generalized Bethe trees. Let be the tree obtained from and the trees by identifying the root vertex of with the vertex of . We give a complete characterization of the eigenvalues of the Laplacian and adjacency matrices of . In particular, we characterize their spectral radii and the algebraic conectivity. Moreover, we derive results concerning their multiplicities. Finally, we apply the results to the case . [Copyright &y& Elsevier]

Details

Language :
English
ISSN :
00243795
Volume :
430
Issue :
1
Database :
Academic Search Index
Journal :
Linear Algebra & its Applications
Publication Type :
Academic Journal
Accession number :
34982156
Full Text :
https://doi.org/10.1016/j.laa.2008.08.009