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...
| Autores: | , , , |
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| 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 |
| 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. |
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