On the Outer-Independent Roman Domination in Graphs

[EN] Let G be a graph with no isolated vertex and f:V(G)->{0,1,2} a function. Let V-i={v is an element of V(G):f(v)=i} for every i is an element of{0,1,2}. The function f is an outer-independent Roman dominating function on G if V0 is an independent set and every vertex in V-0 is adjacent to...

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Detalhes bibliográficos
Autores: Cabrera Martínez, Abel, Cabrera García, Suitberto|||0000-0003-1704-8361, Carrión García, Andrés|||0000-0002-0953-2500, Grisales Del Rio, Angela Maria|||0000-0001-6791-0429
Formato: artículo
Fecha de publicación:2020
País:España
Recursos:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/166744
Acesso em linha:https://riunet.upv.es/handle/10251/166744
Access Level:acceso abierto
Palavra-chave:Outer-independent Roman domination
Roman domination
Vertex cover
Rooted product graph
ESTADISTICA E INVESTIGACION OPERATIVA
Descrição
Resumo:[EN] Let G be a graph with no isolated vertex and f:V(G)->{0,1,2} a function. Let V-i={v is an element of V(G):f(v)=i} for every i is an element of{0,1,2}. The function f is an outer-independent Roman dominating function on G if V0 is an independent set and every vertex in V-0 is adjacent to at least one vertex in V-2. The minimum weight omega(f)= Sigma v is an element of V(G)f(v) among all outer-independent Roman dominating functions f on G is the outer-independent Roman domination number of G. This paper is devoted to the study of the outer-independent Roman domination number of a graph, and it is a contribution to the special issue "Theoretical Computer Science and Discrete Mathematics" of Symmetry. In particular, we obtain new tight bounds for this parameter, and some of them improve some well-known results. We also provide closed formulas for the outer-independent Roman domination number of rooted product graphs.