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Distribution of Laplacian eigenvalues of graphs.
- Source :
-
Linear Algebra & its Applications . Nov2016, Vol. 508, p48-61. 14p. - Publication Year :
- 2016
-
Abstract
- Let G be a graph of order n with m edges and clique number ω . Let μ 1 ≥ μ 2 ≥ … ≥ μ n = 0 be the Laplacian eigenvalues of G and let σ = σ ( G ) ( 1 ≤ σ ≤ n ) be the largest positive integer such that μ σ ≥ 2 m n . In this paper we study the relation between σ and ω . In particular, we provide the answer to Problem 2.3 raised in Pirzada and Ganie (2015) [15] . Moreover, we characterize all connected threshold graphs with σ < ω − 1 , σ = ω − 1 and σ > ω − 1 . We obtain Nordhaus–Gaddum-type results for σ . Some relations between σ with other graph invariants are obtained. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 508
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 117837457
- Full Text :
- https://doi.org/10.1016/j.laa.2016.06.039