• ON THE p-DOMINATION NUMBER AND p-REINFORCEMENT NUMBER OF THE JOIN OF SOME GRAPHS

Abstract

Let  be a graph. A subset D of G is a p-dominating set of G if  for all , where  is the set of all vertices which are adjacent to x.  The p-domination number of G, denoted by , is the minimum cardinality of p-dominating sets of G. The p-reinforcement number of G, denoted by , is the minimum number of edges in  that has to be added to G in order to reduce the p-domination number of the resulting graphs. In this study, we gave a tight upperbound for the p-domination number of the join of graphs, the p-domination number of a complete and any graph, the 2-domination number and 3-domination number of fans, and the 2-reinforcement number and 3-reinforcement number of fans.