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On the Aα-spectra of trees.
- Source :
-
Linear Algebra & its Applications . May2017, Vol. 520, p286-305. 20p. - Publication Year :
- 2017
-
Abstract
- Let G be a graph with adjacency matrix A ( G ) and let D ( G ) be the diagonal matrix of the degrees of G . For every real α ∈ [ 0 , 1 ] , define the matrix A α ( G ) as A α ( G ) = α D ( G ) + ( 1 − α ) A ( G ) . This paper gives several results about the A α -matrices of trees. In particular, it is shown that if T Δ is a tree of maximal degree Δ, then the spectral radius of A α ( T Δ ) satisfies the tight inequality ρ ( A α ( T Δ ) ) < α Δ + 2 ( 1 − α ) Δ − 1 , which implies previous bounds of Godsil, Lovász, and Stevanović. The proof is deduced from some new results about the A α -matrices of Bethe trees and generalized Bethe trees. In addition, several bounds on the spectral radius of A α of general graphs are proved, implying tight bounds for paths and Bethe trees. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 520
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 121378814
- Full Text :
- https://doi.org/10.1016/j.laa.2017.01.029