Partial Domination in Graphs

Let G=(V,E) be a graph. For some alpha with 0<alpha <= 1, a subset S of V is said to be a alpha-partial dominating set if |N[S]|>=alpha|V|. The size of a smallest such S is called the alpha-partial domination number and is denoted by pd alpha(G). In this paper, we introduce alpha-partial domination number in a graph G and study different bounds on the partial domination number of a graph G with respect to its order, maximum degree, domination number etc., Moreover, alpha-partial domination spectrum is introduced and Nordhaus-Gaddum bounds on the partial domination number are studied.