Edge open packing sets in graphs

In a graph G = (V, E), two edges e1 and e2 are said to have a common edge if there exists an edge e ∈ E(G) different from e1 and e2 such that e joins a vertex of e1 to a vertex of e2 in G. That is, 〈e1, e, e2〉 is either P4 or K3 in G. A non-empty set D ⊆ E(G) is an edge open packing set of a graph G if no two edges of D have a common edge in G. The maximum cardinality of an edge open packing set is the edge open packing number of G and is denoted by ${\rho }_e^o(G)$. In this paper, we initiate a study on this parameter