On sum of powers of the Laplacian and signless Laplacian eigenvalues of graphs
type: Item
instance of: scholarly article
title: On sum of powers of the Laplacian and signless Laplacian eigenvalues of graphs
zbMATH Open document ID: 1218.05086
author: Jack H. Koolen
author: Mohammad Reza Oboudi
author: S. Akbari
author: E. Ghorbani
published in: The Electronic Journal of Combinatorics
publication date: 2010-10-13T00:00:00Z
full work available at URL: https://eudml.org/doc/223966
full work available at URL: v17i1r115.html
review text: Let \(G\) be a graph of order \(n\) with signless Laplacian eigenvalues \(q_{1},\dots ,q_{n}\) and Laplacian eigenvalues \(\mu_{1},\dots ,\mu_{n}\). It is proved that for any real number \(\alpha\) with \(0<\alpha \leq 1\) or \(2\leq \alpha <3\), the inequality \(q_{1}^\alpha+\dots + q_{n}^\alpha\geq \mu_{1}^\alpha+\dots + \mu_{n}^\alpha\) holds, and for any real number \(\beta \) with \(1<\beta<2\), the inequality \(q_{1}^\beta +\dots + q_{n}^\beta\geq \mu_{1}^\beta +\dots + \mu_{n}^\beta\) holds. In both inequalities, the equality is attained (for \(\alpha \notin \{1,2\})\) if and only if \(G\) is bipartite.
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 5799443
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5799443