A relation between the Laplacian and signless Laplacian eigenvalues of a graph
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- Title
- A relation between the Laplacian and signless Laplacian eigenvalues of a graph
- Authors
- Akbari, S; Ghorbani, E; Koolen, JH; Oboudi, MR
- Date Issued
- 2010-11
- Publisher
- SPRINGER
- Abstract
- Let G be a graph of order n such that Sigma(n)(i)=0(-1) (i)a(i)gimel(n-i) and Sigma(n)(i=0)(-1)(i)b(i)gimel(n-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 a, 0 < alpha <= 1, if q(1), ... , q(n) and mu(1), ... ,mu(n) are the signless Laplacian and the Laplacian eigenvalues of G, respectively, then q(1)(alpha) + ... + q(n)(alpha) >= mu(alpha)(1) + ... + mu(alpha)(n).
- Keywords
- Laplacian; Signless Laplacian; Incidence energy; Laplacian-like energy; INCIDENCE ENERGY
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/25568
- DOI
- 10.1007/S10801-010-0225-9
- ISSN
- 0925-9899
- Article Type
- Article
- Citation
- JOURNAL OF ALGEBRAIC COMBINATORICS, vol. 32, no. 3, page. 459 - 464, 2010-11
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