Quasiperfect domination in trees
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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.
CitationCáceres, José, Hernando, M., Mora, M., Pelayo, I. M., Puertas, M. Luz. Quasiperfect domination in trees. "Electronic notes in discrete mathematics", 18 Desembre 2015, vol. 50, p. 439-444.