Point-set domination number of a semigraph

A semigraph is a generalization of a graph, and point-set domination is a generalization of domination. The notion of a semigraph is the generalization of a graph, which is different from the generalization of graphs called hypergraphs. In this paper, we characterize the point-set domination number for certain classes of semigraphs, as well as a realization theorem connecting the point-set domination number, a-domination number, and independence number for the semigraph. We find a Nordhaus–Gaddum-type result involving the point-set domination of the semigraph.