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Normalized Laplacian eigenvalues with chromatic number and independence number of graphs.
- Source :
-
Linear & Multilinear Algebra . Jan2020, Vol. 68 Issue 1, p63-80. 18p. - Publication Year :
- 2020
-
Abstract
- Let ρ 1 ≥ ρ 2 ≥ ⋯ ≥ ρ n − 1 ≥ ρ n = 0 be the normalized Laplacian eigenvalues of a graph G with n vertices. Also, let χ and α be the chromatic number and the independence number of a graph G, respectively. In this paper, we discuss some properties of graphs with ρ 1 = χ / (χ − 1). In particular, we characterize all the graphs with ρ 1 = χ / (χ − 1) when the maximum degree is n−1. Moreover, we obtain an upper bound on the multiplicity of normalized Laplacian eigenvalues m G (ρ) in terms of n and α, and also characterize graphs for which the bound is attained. [ABSTRACT FROM AUTHOR]
- Subjects :
- *EIGENVALUES
*MULTIPLICITY (Mathematics)
Subjects
Details
- Language :
- English
- ISSN :
- 03081087
- Volume :
- 68
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Linear & Multilinear Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 139899811
- Full Text :
- https://doi.org/10.1080/03081087.2018.1498827