Graphs With All But Two Eigenvalues In [−2, 0]

Graphs With All But Two Eigenvalues In [−2, 0]

The eigenvalues of a graph are those of its adjacency matrix. Recently, Cioabă, Haemers and Vermette characterized all graphs with all but two eigenvalues equal to −2 and 0. In this article, we extend their result by characterizing explicitly all graphs with all but two eigenvalues in the interval [...

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Main Authors: Abreu Nair, Alencar Jorge, Brondani André, de Lima Leonardo, Oliveira Carla
Format: Article
Language:English
Published: Sciendo 2020-05-01
Series:Discussiones Mathematicae Graph Theory
Subjects:
graph spectrum
complete multipartite graph
graph determined by its spectrum
05c50
Online Access:https://doi.org/10.7151/dmgt.2286
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spelling doaj-af53bfa58a0f40699d89f32a871ae2802021-09-05T17:20:25ZengSciendoDiscussiones Mathematicae Graph Theory2083-58922020-05-0140237939110.7151/dmgt.2286dmgt.2286Graphs With All But Two Eigenvalues In [−2, 0]Abreu Nair0Alencar Jorge1Brondani André2de Lima Leonardo3Oliveira Carla4Production Engineering Department COPPE-UFRJ, Rio de Janeiro, BrazilFederal Institute of Education Science and Technology of Triângulo Mineiro, Minas Gerais, BrazilDepartment of Mathematics, Federal Fluminense University, Volta Redonda, BrazilDepartment of Business, Federal University of Paraná, Paraná, BrazilNational School of Statistical Sciences ENCE-IBGE, Rio de Janeiro, BrazilThe eigenvalues of a graph are those of its adjacency matrix. Recently, Cioabă, Haemers and Vermette characterized all graphs with all but two eigenvalues equal to −2 and 0. In this article, we extend their result by characterizing explicitly all graphs with all but two eigenvalues in the interval [−2, 0]. Also, we determine among them those that are determined by their spectrum.https://doi.org/10.7151/dmgt.2286graph spectrumcomplete multipartite graphgraph determined by its spectrum05c50
collection DOAJ
language English
format Article
sources DOAJ
author Abreu Nair
Alencar Jorge
Brondani André
de Lima Leonardo
Oliveira Carla
spellingShingle Abreu Nair
Alencar Jorge
Brondani André
de Lima Leonardo
Oliveira Carla
Graphs With All But Two Eigenvalues In [−2, 0]
Discussiones Mathematicae Graph Theory
graph spectrum
complete multipartite graph
graph determined by its spectrum
05c50
author_facet Abreu Nair
Alencar Jorge
Brondani André
de Lima Leonardo
Oliveira Carla
author_sort Abreu Nair
title Graphs With All But Two Eigenvalues In [−2, 0]
title_short Graphs With All But Two Eigenvalues In [−2, 0]
title_full Graphs With All But Two Eigenvalues In [−2, 0]
title_fullStr Graphs With All But Two Eigenvalues In [−2, 0]
title_full_unstemmed Graphs With All But Two Eigenvalues In [−2, 0]
title_sort graphs with all but two eigenvalues in [−2, 0]
publisher Sciendo
series Discussiones Mathematicae Graph Theory
issn 2083-5892
publishDate 2020-05-01
description The eigenvalues of a graph are those of its adjacency matrix. Recently, Cioabă, Haemers and Vermette characterized all graphs with all but two eigenvalues equal to −2 and 0. In this article, we extend their result by characterizing explicitly all graphs with all but two eigenvalues in the interval [−2, 0]. Also, we determine among them those that are determined by their spectrum.
topic graph spectrum
complete multipartite graph
graph determined by its spectrum
05c50
url https://doi.org/10.7151/dmgt.2286
work_keys_str_mv AT abreunair graphswithallbuttwoeigenvaluesin20
AT alencarjorge graphswithallbuttwoeigenvaluesin20
AT brondaniandre graphswithallbuttwoeigenvaluesin20
AT delimaleonardo graphswithallbuttwoeigenvaluesin20
AT oliveiracarla graphswithallbuttwoeigenvaluesin20
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