z-DOMINATION IN GRAPHS

Nanet Altubar Goles, Enrico Limbo Enriquez, Carmelita Magdalunes Loquias, Grace Morta Estrada, Romeo C. Alota

Abstract


Let be a connected simple graph. A subset of a vertex setis a dominating set of if for every vertex there exists a vertexsuch thatis an edge of Let  be a minimum dominating set in The dominating set is called an inverse dominating set with respect to A disjoint dominating set of  is the setA -dominating set ofis a disjoint set such that The -domination number denoted by z is the minimum cardinality of -dominating set of -dominating set of  with cardinality equal to  z is called a z-of In this paper,  we show that every even integer and integer with  is realizable as -domination number and order ofrespectively. Further, we characterize the-dominating sets in the join and corona of two graphs and give some important results.

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