TY - JOUR

T1 - Multiplicities of distance Laplacian eigenvalues and forbidden subgraphs

AU - Fernandes, Rosário

AU - de Freitas, Maria Aguieiras A.

AU - Silva, Celso M. da

AU - Del-Vecchio, Renata R.

N1 - info:eu-repo/grantAgreement/FCT/5876/147204/PT#
This work was partially supported by National Counsel of Technological and Scientific Development (CNPq-Conselho Nacional de Desenvolvimento Cientifico e Tecnologico) and FAPERJ (Fundacao de Amparo a Pesquisa do Estado do Rio de Janeiro).
This work was partially supported by National Counsel of Technological and Scientific Development (CNPq-Conselho Nacional de Desenvolvimento Cientifico e Tecnologico).
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PY - 2018/3/15

Y1 - 2018/3/15

N2 - In this work, the graphs of order n having the second distance Laplacian eigenvalue of multiplicity n−2 are determined. Besides that, this result also characterizes the graphs where the multiplicity of some distance Laplacian eigenvalue is equal to n−2. In addition, all connected graphs of order n where the largest eigenvalue of the distance Laplacian matrix has multiplicity n−3 are determined. Finally, we determine some graphs with a distance Laplacian eigenvalue having multiplicity n−3.

AB - In this work, the graphs of order n having the second distance Laplacian eigenvalue of multiplicity n−2 are determined. Besides that, this result also characterizes the graphs where the multiplicity of some distance Laplacian eigenvalue is equal to n−2. In addition, all connected graphs of order n where the largest eigenvalue of the distance Laplacian matrix has multiplicity n−3 are determined. Finally, we determine some graphs with a distance Laplacian eigenvalue having multiplicity n−3.

KW - Distance Laplacian matrix

KW - Laplacian matrix

KW - Multiplicity of eigenvalues

UR - http://www.scopus.com/inward/record.url?scp=85037532398&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2017.11.031

DO - 10.1016/j.laa.2017.11.031

M3 - Article

AN - SCOPUS:85037532398

VL - 541

SP - 81

EP - 93

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

SN - 0024-3795

ER -