Abstract :
In a graph G = (V, E), a subset S ⊆ V (G) is said to be an open packing set of G if no two vertices of S have a common neighbour in G. The maximum cardinality of an open packing set is called the open packing number of G and is denoted by ρ ° (G). This parameter has been studied in [5], [6], [7] and [8]. In this paper, we characterize the graphs G with ρ ° (G) = n − 2, ρ ° (G) = n − ω(G) and ρ ° (G) = n − ∆(G), where n, ω(G) and ∆(G) denote the order, clique number and the maximum degree of G. Also, we discuss the open packing number for split graphs.
