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

EARL JUDE FRANCIS T. AWING*, MICHAEL P. BALDADO, Jr., JOEL G. ADANZA

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.


Keywords


p-dominating set, p-domination number, p-reinforcement number, join, fans.

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