On graphs whose smallest eigenvalue is at least \(-1-\sqrt 2\)
type: Item
instance of: scholarly article
title: On graphs whose smallest eigenvalue is at least \(-1-\sqrt 2\)
zbMATH Open document ID: 0832.05076
DOI: 10.1016/0024-3795(95)00245-M
author: Renee Woo
author: Arnold Neumaier
published in: Linear Algebra and its Applications
publication date: 1995-10-26T00:00:00Z
review text: This paper shows that if the smallest eigenvalue of a graph \(H\) exceeds a fixed number larger than the smallest root \((\approx- 2.4812)\) of the polynomial \(x^3+ 2x^2- 2x- 2\), and if every vertex of \(H\) has sufficiently large valency, then the smallest eigenvalue of \(H\) is at least \(-1-\sqrt 2\) and the structure of \(H\) is completely characterized through a new generalization of line graphs.
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 803762
zbMATH Keywords: smallest eigenvalue
zbMATH Keywords: line graphs
MaRDI profile type: Publication
cites work: Q3992965
cites work: Exceptional graphs with smallest eigenvalue -2 and related problems
cites work: Line graphs, root systems, and elliptic geometry
cites work: Q3997075
cites work: On graphs whose least eigenvalue exceeds \(-1-\sqrt2\)
cites work: Strongly regular graphs with smallest eigenvalue -m
cites work: Graph representations, two-distance sets, and equiangular lines
description: scientific article; zbMATH DE number 803762