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A relation between the Laplacian and signless Laplacian eigenvalues of a graph

Akbari, S ; Sharif University of Technology | 2010

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  1. Type of Document: Article
  2. DOI: 10.1007/s10801-010-0225-9
  3. Publisher: 2010
  4. Abstract:
  5. Let G be a graph of order n such that ∑n i=0(-1) iailambdan-i and ∑n i=0(-1) iailambdan-i are the characteristic polynomials of the signless Laplacian and the Laplacian matrices of G, respectively. We show that a i ≥b i for i=0,1,⋯,n. As a consequence, we prove that for any α, 0<α≤1, if q 1,⋯,q n and μ 1,⋯,μ n are the signless Laplacian and the Laplacian eigenvalues of G, respectively, then q 1 alpha+⋯+qα n≥μ α 1+⋯+μα n
  6. Keywords:
  7. Incidence energy ; Laplacian ; Laplacian-like energy ; Signless Laplacian ; Characteristic polynomials ; Laplacian eigenvalues ; Laplacian matrices ; Laplacians ; Eigenvalues and eigenfunctions ; Laplace transforms
  8. Source: Journal of Algebraic Combinatorics ; Volume 32, Issue 3 , 2010 , Pages 459-464 ; 09259899 (ISSN)
  9. URL: http://link.springer.com/article/10.1007%2Fs10801-010-0225-9