Uniformly Optimally Reliable Graphs: A Survey

Which is the most reliable graph with n nodes and m edges? This celebrated problem has several aspects, according to the notion of optimality (in a local or uniform sense), failure type (either nodes or edges), or reliability model (all-terminal connectedness, two-terminal or multiterminal setting)....

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Detalhes bibliográficos
Autor: Romero, Pablo
Formato: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2021
País:Uruguay
Recursos:Agencia Nacional de Investigación e Innovación
Repositorio:REDI
Idioma:inglés
OAI Identifier:oai:redi.anii.org.uy:20.500.12381/699
Acesso em linha:https://hdl.handle.net/20.500.12381/699
Access Level:acceso abierto
Palavra-chave:Uniformly most reliable graph
Uniformly least reliable graph
All-terminal reliability
Two-terminal reliability
Failure type
Graph theory
Ciencias Naturales y Exactas
Matemáticas
Matemática Aplicada
Descrição
Resumo:Which is the most reliable graph with n nodes and m edges? This celebrated problem has several aspects, according to the notion of optimality (in a local or uniform sense), failure type (either nodes or edges), or reliability model (all-terminal connectedness, two-terminal or multiterminal setting). This article presents a chronological survey of the multiple proposals to address the problem, together with recent trends and enigmatic conjectures posed decades ago that promote further research.