Open-independent, open-locating-dominating sets

Suk J. Seo (Computer Science Department, Middle Tennessee State University, Murfreesboro, TN 37132, U.S.A)
Peter J. Slater (Mathematical Sciences Department and Computer Science Department, University of Alabama in Huntsville, Huntsville, AL 35899, U.S.A)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 5, No 2 (2017): Electronic Journal of Graph Theory and Applications

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.