z-DOMINATION IN GRAPHS - Goles, Nanet Altubar; Enriquez, Enrico Limbo; Loquias, Carmelita Magdalunes; Estrada, Grace Morta; Alota, Romeo C. (Journal of Global Research in Mathematical Archives(JGRMA), 2018)
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.