Open Packing in Graphs

Let \(G\) be a graph and let \(S\) be a subset of vertices of \(G\). The open neighborhood of a vertex \(v\) of \(G\) is the set of all vertices adjacent to \(v\) in \(G\). The set \(S\) is an open packing of \(G\) if the open neighborhoods of the vertices of \(S\) are pairwise disjoint in \(G\). The lower open packing number of \(G\), denoted \(\rho_L^o(G)\), is the minimum cardinality of a maximal open packing of \(G\), while the (upper) open packing number of \(G\), denoted \(\rho^o(G)\), is the maximum cardinality among all open packings of \(G\). In this paper, we present theoretical and computational
results for the open packing numbers of a graph.