On the multiplicities of distance Laplacian eigenvalues

Rosário Fernandes; Maria A. A. de Freitas; Celso M.  da Silva Jr.; Renata R. Del-Vecchio

doi:10.1007/s40314-023-02460-1

On the multiplicities of distance Laplacian eigenvalues

Rosário Fernandes, Maria A. A. de Freitas, Celso M. da Silva Jr., Renata R. Del-Vecchio

Research output: Contribution to journal › Article › peer-review

Abstract

In this work, connected graphs of order n and largest eigenvalue of the distance Laplacian matrix with multiplicity equal to n- 4 are investigated. A complete characterization is presented if n is one of its distance Laplacian eigenvalues with multiplicity one. We also present a conjecture about forbidden subgraphs of G when the multiplicity of its largest eigenvalue is n- 4 , and we analyze the case where G has diameter four.

Original language	English
Article number	317
Number of pages	16
Journal	Computational and Applied Mathematics
Volume	42
Issue number	7
DOIs	https://doi.org/10.1007/s40314-023-02460-1
Publication status	Published - Oct 2023

Keywords

Distance Laplacian matrix
Laplacian matrix
Multiplicity of eigenvalues

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10.1007/s40314-023-02460-1

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@article{c262022bbd3d48378e92670f98ba3f21,

title = "On the multiplicities of distance Laplacian eigenvalues",

abstract = "In this work, connected graphs of order n and largest eigenvalue of the distance Laplacian matrix with multiplicity equal to n- 4 are investigated. A complete characterization is presented if n is one of its distance Laplacian eigenvalues with multiplicity one. We also present a conjecture about forbidden subgraphs of G when the multiplicity of its largest eigenvalue is n- 4 , and we analyze the case where G has diameter four.",

keywords = "Distance Laplacian matrix, Laplacian matrix, Multiplicity of eigenvalues",

author = "Ros{\'a}rio Fernandes and {de Freitas}, {Maria A. A.} and {da Silva Jr.}, {Celso M.} and Del-Vecchio, {Renata R.}",

note = "Funding Information: info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00297%2F2020/PT# The research of the second, third and fourth author is partially supported by the National Council for Scientific and Technological Development (CNPq) with CNPq Grant 313335/2020-6; CNPq Grant 403963/2021-4; CNPq Grant 306262/2019-3 and CNPq Grant 403963/2021-4, respectively. The research of the third author is partially supported by FAPERJ with Grant E-20/2022-284573. Publisher Copyright: {\textcopyright} 2023, The Author(s) under exclusive licence to Sociedade Brasileira de Matem{\'a}tica Aplicada e Computacional.",

year = "2023",

month = oct,

doi = "10.1007/s40314-023-02460-1",

language = "English",

volume = "42",

journal = "Computational and Applied Mathematics",

issn = "2238-3603",

publisher = "Birkhauser Boston",

number = "7",

}

TY - JOUR

T1 - On the multiplicities of distance Laplacian eigenvalues

AU - Fernandes, Rosário

AU - de Freitas, Maria A. A.

AU - da Silva Jr., Celso M.

AU - Del-Vecchio, Renata R.

N1 - Funding Information: info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00297%2F2020/PT# The research of the second, third and fourth author is partially supported by the National Council for Scientific and Technological Development (CNPq) with CNPq Grant 313335/2020-6; CNPq Grant 403963/2021-4; CNPq Grant 306262/2019-3 and CNPq Grant 403963/2021-4, respectively. The research of the third author is partially supported by FAPERJ with Grant E-20/2022-284573. Publisher Copyright: © 2023, The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional.

PY - 2023/10

Y1 - 2023/10

N2 - In this work, connected graphs of order n and largest eigenvalue of the distance Laplacian matrix with multiplicity equal to n- 4 are investigated. A complete characterization is presented if n is one of its distance Laplacian eigenvalues with multiplicity one. We also present a conjecture about forbidden subgraphs of G when the multiplicity of its largest eigenvalue is n- 4 , and we analyze the case where G has diameter four.

AB - In this work, connected graphs of order n and largest eigenvalue of the distance Laplacian matrix with multiplicity equal to n- 4 are investigated. A complete characterization is presented if n is one of its distance Laplacian eigenvalues with multiplicity one. We also present a conjecture about forbidden subgraphs of G when the multiplicity of its largest eigenvalue is n- 4 , and we analyze the case where G has diameter four.

KW - Distance Laplacian matrix

KW - Laplacian matrix

KW - Multiplicity of eigenvalues

UR - http://www.scopus.com/inward/record.url?scp=85173575255&partnerID=8YFLogxK

U2 - 10.1007/s40314-023-02460-1

DO - 10.1007/s40314-023-02460-1

M3 - Article

AN - SCOPUS:85173575255

SN - 2238-3603

VL - 42

JO - Computational and Applied Mathematics

JF - Computational and Applied Mathematics

IS - 7

M1 - 317

ER -

On the multiplicities of distance Laplacian eigenvalues

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