The Gross-Saccoman Conjecture is True
Consider a graph with perfect nodes but independent edge failures with identical probability ρ. The reliability is the connectedness probability of the random graph. A graph with n nodes and e edges is uniformly optimally reliable (UOR) if it has the greatest reliability among all graphs with the sa...
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| Format: | article |
| Language: | English |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://hdl.handle.net/20.500.12381/700 |
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| _version_ | 1868889964628934656 |
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| author | Romero, Pablo |
| author_browse | Romero, Pablo |
| author_facet | Romero, Pablo |
| author_role | author |
| collection | REDI |
| dc.creator.none.fl_str_mv | Romero, Pablo |
| dc.date.none.fl_str_mv | 2020-11-24 2022-10-20T23:29:04Z |
| dc.identifier.none.fl_str_mv | https://hdl.handle.net/20.500.12381/700 FCE_1_2019_1_156693 10.1002/net.22006 |
| dc.language.none.fl_str_mv | eng |
| dc.publisher.none.fl_str_mv | Wiley |
| dc.rights.none.fl_str_mv | Acceso abierto info:eu-repo/semantics/openAccess Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional. (CC BY-NC-ND) 2023-09-30 2022-11-24 |
| dc.source.none.fl_str_mv | Networks reponame:REDI instname:Agencia Nacional de Investigación e Innovación instacron:Agencia Nacional de Investigación e Innovación |
| dc.subject.none.fl_str_mv | Graph Theory Uniformly optimally reliable graph Gross-Saccoman conjecture Network Reliability Optimization Multigraphs Ciencias Naturales y Exactas Matemáticas Matemática Aplicada |
| dc.title.none.fl_str_mv | The Gross-Saccoman Conjecture is True |
| dc.type.none.fl_str_mv | Artículo info:eu-repo/semantics/article Enviado info:eu-repo/semantics/submittedVersion |
| description | Consider a graph with perfect nodes but independent edge failures with identical probability ρ. The reliability is the connectedness probability of the random graph. A graph with n nodes and e edges is uniformly optimally reliable (UOR) if it has the greatest reliability among all graphs with the same number of nodes and edges, for all values of ρ. In 1997, Gross and Saccoman proved that the simple UOR graphs for e = n, e = n + 1 and e = n + 2 are also optimal when the classes are extended to include multigraphs [6]. The authors conjectured that the UOR simple graphs for e = n + 3 are optimal in multigraphs as well. A proof of the Gross-Saccoman conjecture is introduced. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | anni_149ec9d9d78c9c3a19ee98fa55d0c8be |
| identifier_str_mv | FCE_1_2019_1_156693 10.1002/net.22006 |
| instacron_str | Agencia Nacional de Investigación e Innovación |
| institution | Agencia Nacional de Investigación e Innovación |
| instname_str | Agencia Nacional de Investigación e Innovación |
| language | eng |
| network_acronym_str | anni |
| network_name_str | oai-lr-anni |
| oai_identifier_str | oai:redi.anii.org.uy:20.500.12381/700 |
| publishDate | 2020 |
| publishDateSort | 2020 |
| publisher.none.fl_str_mv | Wiley |
| reponame_str | REDI |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| rights_invalid_str_mv | Acceso abierto Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional. (CC BY-NC-ND) 2023-09-30 2022-11-24 |
| spelling | The Gross-Saccoman Conjecture is TrueRomero, PabloGraph TheoryUniformly optimally reliable graphGross-Saccoman conjectureNetwork ReliabilityOptimizationMultigraphsCiencias Naturales y ExactasMatemáticasMatemática AplicadaConsider a graph with perfect nodes but independent edge failures with identical probability ρ. The reliability is the connectedness probability of the random graph. A graph with n nodes and e edges is uniformly optimally reliable (UOR) if it has the greatest reliability among all graphs with the same number of nodes and edges, for all values of ρ. In 1997, Gross and Saccoman proved that the simple UOR graphs for e = n, e = n + 1 and e = n + 2 are also optimal when the classes are extended to include multigraphs [6]. The authors conjectured that the UOR simple graphs for e = n + 3 are optimal in multigraphs as well. A proof of the Gross-Saccoman conjecture is introduced.Agencia Nacional de Investigación e InnovaciónWiley2022-10-20T23:29:04Z2020-11-24Artículoinfo:eu-repo/semantics/articleEnviadoinfo:eu-repo/semantics/submittedVersionhttps://hdl.handle.net/20.500.12381/700FCE_1_2019_1_15669310.1002/net.22006Networksreponame:REDIinstname:Agencia Nacional de Investigación e Innovacióninstacron:Agencia Nacional de Investigación e InnovaciónengAcceso abiertoinfo:eu-repo/semantics/openAccessReconocimiento-NoComercial-SinObraDerivada 4.0 Internacional. (CC BY-NC-ND)2023-09-302022-11-24oai:redi.anii.org.uy:20.500.12381/7002026-06-16T05:02:34Z |
| spellingShingle | The Gross-Saccoman Conjecture is True Romero, Pablo Graph Theory Uniformly optimally reliable graph Gross-Saccoman conjecture Network Reliability Optimization Multigraphs Ciencias Naturales y Exactas Matemáticas Matemática Aplicada |
| status_str | submittedVersion |
| title | The Gross-Saccoman Conjecture is True |
| title_full | The Gross-Saccoman Conjecture is True |
| title_fullStr | The Gross-Saccoman Conjecture is True |
| title_full_unstemmed | The Gross-Saccoman Conjecture is True |
| title_short | The Gross-Saccoman Conjecture is True |
| title_sort | The Gross-Saccoman Conjecture is True |
| topic | Graph Theory Uniformly optimally reliable graph Gross-Saccoman conjecture Network Reliability Optimization Multigraphs Ciencias Naturales y Exactas Matemáticas Matemática Aplicada |
| url | https://hdl.handle.net/20.500.12381/700 |