WHOLE DOMINATION IN GRAPHS - Omran, Ahmed A; Ibrahim, Thaer A (TWMS journal of applied and engineering mathematics, 2022)
In this paper, a new parameter of domination number in graphs is defined which is called whole domination number denoted by [[gamma].sub.wh](G). Some bounds of whole domination number and the number of edges depend on it has been established. Furthermore, the effect of deletion vertex, edge, or add edge have been studied. Also, the effect of the contracting an edge is determined. Finally, some operations between the two graphs have been calculated. Keywords: Whole dominating set, Whole domination number, Deletion, Contracting an edge. AMS Subject Classification: 05C69.