Open packing subdivision number of graphs

Abstract

A nonempty set [Formula: see text] of a graph [Formula: see text] is an open packing set of [Formula: see text] if no two vertices of [Formula: see text] have a common neighbor in [Formula: see text]. The maximum cardinality of an open packing set is called the open packing number of [Formula: see text] and is denoted by [Formula: see text]. The open packing subdivision number [Formula: see text] is the minimum number of edges in [Formula: see text] that must be subdivided (each edge in [Formula: see text] can be subdivided at most once) in order to increase the open packing number. In this paper, we initiate a study on this parameter.