WEAKLY CONVEX DOUBLY CONNECTED DOMINATION IN THE JOIN AND CORONA OF GRAPHS - Enriquez, Enrico Limbo; Estrada, Grace M.; Loquias, Carmelita M. (Journal of Global Research in Mathematical Archives(JGRMA), 2018)
Let be a connected simple graph. A weakly convex dominating set Â of is a weakly convex doubly connected dominating set if Â is a doubly connected dominating set of The weakly convex doubly connected domination number of Â denoted by , is the smallest cardinality of a convex doubly connected dominating set Â of . In this paper, we show that for each set of integers and Â with the integers Â and Â are realizable as weakly convex doubly connected domination number, convex doubly connected domination number, and order of , respectively. Further, we give the characterization of the weakly convex doubly connected dominating set with weakly convex doubly connected domination numbers of 1 and 2. Finally, we characterize the weakly convex doubly connected dominating sets of the join and corona of two graphs.