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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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2020 |
| País: | Uruguay |
| Institución: | Agencia Nacional de Investigación e Innovación |
| Repositorio: | REDI |
| Idioma: | inglés |
| OAI Identifier: | oai:redi.anii.org.uy:20.500.12381/700 |
| Acceso en línea: | https://hdl.handle.net/20.500.12381/700 |
| Access Level: | acceso abierto |
| Palabra clave: | Graph Theory Uniformly optimally reliable graph Gross-Saccoman conjecture Network Reliability Optimization Multigraphs Ciencias Naturales y Exactas Matemáticas Matemática Aplicada |
| Sumario: | 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. |
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