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Spectra of generalized Bethe trees attached to a path

โœ Scribed by Oscar Rojo; Luis Medina

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
238 KB
Volume
430
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

A generalized Bethe tree is a rooted tree in which vertices at the same distance from the root have the same degree. Let P m be a path of m vertices. Let {B i : 1 i m} be a set of generalized Bethe trees. Let P m {B i : 1 i m} be the tree obtained from P m and the trees B 1 , B 2 , . . . , B m by identifying the root vertex of B i with the ith vertex of P m . We give a complete characterization of the eigenvalues of the Laplacian and adjacency matrices of P m {B i : 1 i m}. 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

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