WEAKLY CONVEX DOUBLY CONNECTED DOMINATION IN THE JOIN AND CORONA OF GRAPHS
Enrico L. Enriquez, Grace M. Estrada -, Carmelita M. Loquias · Journal of Global Research in Mathematical Archives(JGRMA) · 2018
Let be a connected simple graph. A weakly convex dominating set of is a weakly convex doubly connected dominating set if is a doubly connected dominating set of The weakly convex doubly connected domination number of denoted by , is the smallest cardinality of a convex doubly connected dominating set of . In this paper, we show that for each set of integers and with the integers and 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.