Open-independent, open-locating-dominating sets

• Main Authors: Suk J. Seo, Peter J. Slater
• Format: Article
• Language: English
• Published: Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia 2017-10-01
• Series: Electronic Journal of Graph Theory and Applications
• Subjects: distinguishing sets, open-independent sets, open-locating-dominating sets, open-independent, open-locating-dominating sets
• Online Access: https://www.ejgta.org/index.php/ejgta/article/view/210

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.