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 ofÂ if for every vertex there exists a vertexsuch thatis an edge ofÂ Let Â be a minimum dominating set in The dominating set is called an inverse dominating set with respect toÂ A disjoint dominating set of Â is the setA -dominating set ofis a disjoint set such that The -domination number denoted by zÂ is the minimum cardinality of -dominating set of -dominating set of Â with cardinality equal to Â zÂ is called a z-of In this paper,Â we show that every even integer and integerÂ with Â 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.