In this work, two types of codes such that they both dominate and locate the vertices of a graph are studied. Those codes might be sets of detectors in a network or processors controlling a system whose set of responses ...

In this work we study the metric dimension and the location-domination number of maximal outerplanar graphs. Concretely, we determine tight upper and lower bounds on the metric dimension and characterize those maximal ...

A dominating set S of a graph is a metric-locating-dominating set if each vertex of the graph is uniquely distinguished by its distances from the elements of S , and the minimum cardinality of such a set is called the ...

A k -coloring of a graph G is a k -partition ¿ = { S 1 ,...,S k } of V ( G ) into independent sets, called colors . A k -coloring is called neighbor-locating if for every pair of vertices u,v belonging to the same color S ...

A dominating set S of a graph is a metric-locating-dominating set if each vertex of the graph is uniquely distinguished by its distanc es from the elements of S , and the minimum cardinality of such a set is called the ...

Let G be a finite simple connected graph. A vertex v is a boundary vertex of G if there exists a vertex u such that no neighbor of v is further away from u than v. We obtain a number of properties involving different types ...

A dominating set S of a graph G is called locating-dominating, LD-set for short, if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S. Locating-dominating sets of minimum cardinality ...