Quasiperfect domination in trees
A k–quasiperfect dominating set ( k=1k=1) of a graph G is a vertex subset S such that every vertex not in S is adjacent to at least one and at most k vertices in S. The cardinality of a minimum k–quasiperfect dominating set of G is denoted by ¿1k(G)¿1k(G). Those sets were first introduced by Chellal...
| Autores: | , , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/85175 |
| Acceso en línea: | https://hdl.handle.net/2117/85175 https://dx.doi.org/10.1016/j.endm.2015.07.073 |
| Access Level: | acceso abierto |
| Palabra clave: | Graph theory Domination Perfect domination Quasiperfect domination Trees Grafs, Teoria de Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | A k–quasiperfect dominating set ( k=1k=1) of a graph G is a vertex subset S such that every vertex not in S is adjacent to at least one and at most k vertices in S. The cardinality of a minimum k–quasiperfect dominating set of G is denoted by ¿1k(G)¿1k(G). Those sets were first introduced by Chellali et al. (2013) as a generalization of the perfect domination concept (which coincides with the case k=1k=1) and allow us to construct a decreasing chain of quasiperfect dominating parameters ¿11(G)=¿12(G)=…=¿1,¿(G)=¿(G),¿11(G)=¿12(G)=…=¿1,¿(G)=¿(G), (1) in order to indicate how far is G from being perfectly dominated. In this work, we study general properties, tight bounds, existence and realization results involving the parameters of the so-called QP-chain ( 1), for trees. |
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