Open-independent, open-locating-dominating sets - Suk J. Seo; Peter J. Slater (Electronic Journal of Graph Theory and Applications (EJGTA), 2017)
A distinguishing set for a graph G = (V, E) is a dominating set D, each vertex $v \in D$ being the location of some form of a locating device, from which one can detect and precisely identify any given "intruder" vertex in V(G).  As with many applications of dominating sets, the set $D$ might be required to have a certain property for <D>, the subgraph induced by D (such as independence,  paired, or connected).  Recently  the study of independent locating-dominating sets and independent identifying codes was initiated.  Here we introduce the property of open-independence for open-locating-dominating sets.