Restrained double domination in the join and corona of graphs
Arnel M. Cuivillas, Sergio R. Canoy · International Journal of Mathematical Analysis · 2014
A double dominating set ofG is a restrained double dominating set of G if for eachx2 V (G)nS, there existsy2 V (G)nS such thatxy2 E(G). In this paper, we characterized the restrained double dominating sets in the join, and corona of two graphs. We also determine sharp bounds for the restrained double domination numbers of these graphs. In particular, we show that if G and H are any graphs without isolated vertices of orders n and m, respectively, then r 2(G H) = minfn( r(H) + 1);n 2(H)g, where r, 2, and r 2 are, respectively, the restrained domination, double domination, and restrained double domination parameters.