On the spectral radius of the generalized adjacency matrix of a digraph
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10773/35242 |
Resumo: | Let $ D$ be a strongly connected digraph and $\alpha\in [0,1].$ In [J. P. Liu, X. Z. Wu, J. S. Chen and B. L. Liu, The $ A_{\alpha} $ spectral radius characterization of some digraphs, Linear Algebra Appl. 563 (2019) 63--74] the matrix $ A_{\alpha}(D)=\alpha Deg(D)+(1-\alpha)A(D),$ where $ A(D)$ and $Deg(D)$ are the adjacency matrix and the diagonal matrix of the out-degrees of $D,$ respectively, was defined. In this paper it is established some sharp bounds on the $A_{\alpha}(D)$-spectral radius in terms of some parameters such as the out-degrees, the maximum out-degree, the second maximum out-degree, the number of vertices, the number of arcs, the average $2$-outdegrees of the vertices of $D$ and the parameter $ \alpha$ of $A_{\alpha}(D)$. The extremal digraphs attaining these bounds are characterized. It is shown that the bounds obtained improve, in some cases, some of recently given bounds presented in the literature. |
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On the spectral radius of the generalized adjacency matrix of a digraphStrongly connected digraphAdjacency matrixAα-spectral radiusMaximum out-degreeLet $ D$ be a strongly connected digraph and $\alpha\in [0,1].$ In [J. P. Liu, X. Z. Wu, J. S. Chen and B. L. Liu, The $ A_{\alpha} $ spectral radius characterization of some digraphs, Linear Algebra Appl. 563 (2019) 63--74] the matrix $ A_{\alpha}(D)=\alpha Deg(D)+(1-\alpha)A(D),$ where $ A(D)$ and $Deg(D)$ are the adjacency matrix and the diagonal matrix of the out-degrees of $D,$ respectively, was defined. In this paper it is established some sharp bounds on the $A_{\alpha}(D)$-spectral radius in terms of some parameters such as the out-degrees, the maximum out-degree, the second maximum out-degree, the number of vertices, the number of arcs, the average $2$-outdegrees of the vertices of $D$ and the parameter $ \alpha$ of $A_{\alpha}(D)$. The extremal digraphs attaining these bounds are characterized. It is shown that the bounds obtained improve, in some cases, some of recently given bounds presented in the literature.Elsevier2024-11-15T00:00:00Z2022-11-15T00:00:00Z2022-11-15info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/35242eng0024-379510.1016/j.laa.2022.08.017Baghipur, MaryamGanie, Hilal A.Ghorbani, ModjtabaAndrade, Enideinfo:eu-repo/semantics/embargoedAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T12:07:39Zoai:ria.ua.pt:10773/35242Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:06:13.562902Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
On the spectral radius of the generalized adjacency matrix of a digraph |
title |
On the spectral radius of the generalized adjacency matrix of a digraph |
spellingShingle |
On the spectral radius of the generalized adjacency matrix of a digraph Baghipur, Maryam Strongly connected digraph Adjacency matrix Aα-spectral radius Maximum out-degree |
title_short |
On the spectral radius of the generalized adjacency matrix of a digraph |
title_full |
On the spectral radius of the generalized adjacency matrix of a digraph |
title_fullStr |
On the spectral radius of the generalized adjacency matrix of a digraph |
title_full_unstemmed |
On the spectral radius of the generalized adjacency matrix of a digraph |
title_sort |
On the spectral radius of the generalized adjacency matrix of a digraph |
author |
Baghipur, Maryam |
author_facet |
Baghipur, Maryam Ganie, Hilal A. Ghorbani, Modjtaba Andrade, Enide |
author_role |
author |
author2 |
Ganie, Hilal A. Ghorbani, Modjtaba Andrade, Enide |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Baghipur, Maryam Ganie, Hilal A. Ghorbani, Modjtaba Andrade, Enide |
dc.subject.por.fl_str_mv |
Strongly connected digraph Adjacency matrix Aα-spectral radius Maximum out-degree |
topic |
Strongly connected digraph Adjacency matrix Aα-spectral radius Maximum out-degree |
description |
Let $ D$ be a strongly connected digraph and $\alpha\in [0,1].$ In [J. P. Liu, X. Z. Wu, J. S. Chen and B. L. Liu, The $ A_{\alpha} $ spectral radius characterization of some digraphs, Linear Algebra Appl. 563 (2019) 63--74] the matrix $ A_{\alpha}(D)=\alpha Deg(D)+(1-\alpha)A(D),$ where $ A(D)$ and $Deg(D)$ are the adjacency matrix and the diagonal matrix of the out-degrees of $D,$ respectively, was defined. In this paper it is established some sharp bounds on the $A_{\alpha}(D)$-spectral radius in terms of some parameters such as the out-degrees, the maximum out-degree, the second maximum out-degree, the number of vertices, the number of arcs, the average $2$-outdegrees of the vertices of $D$ and the parameter $ \alpha$ of $A_{\alpha}(D)$. The extremal digraphs attaining these bounds are characterized. It is shown that the bounds obtained improve, in some cases, some of recently given bounds presented in the literature. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022-11-15T00:00:00Z 2022-11-15 2024-11-15T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10773/35242 |
url |
http://hdl.handle.net/10773/35242 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0024-3795 10.1016/j.laa.2022.08.017 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/embargoedAccess |
eu_rights_str_mv |
embargoedAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799137717305475072 |