Near threshold graphs
type: Item
instance of: scholarly article
title: Near threshold graphs
zbMATH Open document ID: 1165.05331
published in: The Electronic Journal of Combinatorics
publication date: 2009-07-08T00:00:00Z
full work available at URL: https://eudml.org/doc/130287
full work available at URL: v16i1r42.html
review text: Summary: A conjecture of Grone and Merris states that for any graph \(G\), its Laplacian spectrum, \(\Lambda(G)\), is majorized by its conjugate degree sequence, \(D^*(G)\). That conjecture prompts an investigation of the relationship between \(\Lambda(G)\) and \(D^*(G),\) and Merris has characterized the graphs \(G\) for which the multisets \(\Lambda(G)\) and \(D^*(G)\) are equal. In this paper, we provide a constructive characterization of the graphs \(G\) for which \(\Lambda(G)\) and \(D^*(G)\) share all but two elements.
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 5576423
author: S. J. Kirkland
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5576423