Packing Parameters in Graphs

In a graph $G = (V,E)$, a non-empty set $S ⊆ V$ is said to be an open packing set if no two vertices of $S$ have a common neighbour in $G$. An open packing set which is not a proper subset of any open packing set is called a maximal open packing set. The minimum and maximum cardinalities of a maximal open packing set are respectively called the lower open packing number and the open packing number and are denoted by $ρ^L_o$ and $ρ^o$. In this paper, we present some bounds on these parameters.