Lexicographic polynomials of graphs and their spectra
Autor(a) principal: | |
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Data de Publicação: | 2017 |
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/10773/18640 |
Resumo: | For a (simple) graph $H$ and non-negative integers $c_0,c_1,\ldots,c_d$ ($c_d \neq 0$), $p(H)=\sum_{k=0}^d{c_k \cdot H^k}$ is the lexicographic polynomial in $H$ of degree $d$, where the sum of two graphs is their join and $c_k \cdot H^k$ is the join of $c_k$ copies of $H^k$. The graph $H^k$ is the $k$th power of $H$ with respect to the lexicographic product ($H^0 = K_1$). The spectrum (if $H$ is regular) and the Laplacian spectrum (in general case) of $p(H)$ are determined in terms of the spectrum of $H$ and~$c_k$'s. Constructions of infinite families of cospectral or integral graphs are also announced. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
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Lexicographic polynomials of graphs and their spectraSpectral graph theoryLexicographic productAdjacency and Laplacian matricesCospectral graphsIntegral graphsFor a (simple) graph $H$ and non-negative integers $c_0,c_1,\ldots,c_d$ ($c_d \neq 0$), $p(H)=\sum_{k=0}^d{c_k \cdot H^k}$ is the lexicographic polynomial in $H$ of degree $d$, where the sum of two graphs is their join and $c_k \cdot H^k$ is the join of $c_k$ copies of $H^k$. The graph $H^k$ is the $k$th power of $H$ with respect to the lexicographic product ($H^0 = K_1$). The spectrum (if $H$ is regular) and the Laplacian spectrum (in general case) of $p(H)$ are determined in terms of the spectrum of $H$ and~$c_k$'s. Constructions of infinite families of cospectral or integral graphs are also announced.University of Belgrade2017-10-26T09:26:10Z2017-10-24T00:00:00Z2017-10-24info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/18640eng1452-8630https//10.2298/AADM1702258CCardoso, Domingos M.Carvalho, PaulaRama, PaulaSimic, Slobodan K.Stanic, Zoraninfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T11:36:05Zoai:ria.ua.pt:10773/18640Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:53:35.091381Repositório 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 |
Lexicographic polynomials of graphs and their spectra |
title |
Lexicographic polynomials of graphs and their spectra |
spellingShingle |
Lexicographic polynomials of graphs and their spectra Cardoso, Domingos M. Spectral graph theory Lexicographic product Adjacency and Laplacian matrices Cospectral graphs Integral graphs |
title_short |
Lexicographic polynomials of graphs and their spectra |
title_full |
Lexicographic polynomials of graphs and their spectra |
title_fullStr |
Lexicographic polynomials of graphs and their spectra |
title_full_unstemmed |
Lexicographic polynomials of graphs and their spectra |
title_sort |
Lexicographic polynomials of graphs and their spectra |
author |
Cardoso, Domingos M. |
author_facet |
Cardoso, Domingos M. Carvalho, Paula Rama, Paula Simic, Slobodan K. Stanic, Zoran |
author_role |
author |
author2 |
Carvalho, Paula Rama, Paula Simic, Slobodan K. Stanic, Zoran |
author2_role |
author author author author |
dc.contributor.author.fl_str_mv |
Cardoso, Domingos M. Carvalho, Paula Rama, Paula Simic, Slobodan K. Stanic, Zoran |
dc.subject.por.fl_str_mv |
Spectral graph theory Lexicographic product Adjacency and Laplacian matrices Cospectral graphs Integral graphs |
topic |
Spectral graph theory Lexicographic product Adjacency and Laplacian matrices Cospectral graphs Integral graphs |
description |
For a (simple) graph $H$ and non-negative integers $c_0,c_1,\ldots,c_d$ ($c_d \neq 0$), $p(H)=\sum_{k=0}^d{c_k \cdot H^k}$ is the lexicographic polynomial in $H$ of degree $d$, where the sum of two graphs is their join and $c_k \cdot H^k$ is the join of $c_k$ copies of $H^k$. The graph $H^k$ is the $k$th power of $H$ with respect to the lexicographic product ($H^0 = K_1$). The spectrum (if $H$ is regular) and the Laplacian spectrum (in general case) of $p(H)$ are determined in terms of the spectrum of $H$ and~$c_k$'s. Constructions of infinite families of cospectral or integral graphs are also announced. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017-10-26T09:26:10Z 2017-10-24T00:00:00Z 2017-10-24 |
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/10773/18640 |
url |
http://hdl.handle.net/10773/18640 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1452-8630 https//10.2298/AADM1702258C |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
University of Belgrade |
publisher.none.fl_str_mv |
University of Belgrade |
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) |
collection |
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 |
repository.mail.fl_str_mv |
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1799137587166707712 |