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## Publications

Publications (8)

We study upper bounds on the size of optimum locating-total dominating sets in graphs. A set $S$ of vertices of a graph $G$ is a locating-total dominating set if every vertex of $G$ has a neighbor in $S$, and if any two vertices outside $S$ have distinct neighborhoods within $S$. The smallest size of such a set is denoted by $\gamma^L_t(G)$. It has...

A metric basis in a graph $G$ is a smallest possible set $S$ of vertices of $G$, with the property that any two vertices of $G$ are uniquely recognized by using a vector of distances to the vertices in $S$. A strong metric basis is a variant of metric basis that represents a smallest possible set $S'$ of vertices of $G$ such that any two vertices $...

A set R⊆V(G) is a resolving set of a graph G if for all distinct vertices v,u∈V(G) there exists an element r∈R such that d(r,v)≠d(r,u). The metric dimension dim(G) of the graph G is the cardinality of a smallest resolving set of G. A resolving set with cardinality dim(G) is called a metric basis of G. We consider vertices that are in all metric bas...

A set $R \subseteq V(G)$ is a resolving set of a graph $G$ if for all distinct vertices $v,u \in V(G)$ there exists an element $r \in R$ such that $d(r,v) \neq d(r,u)$. The metric dimension $\dim(G)$ of the graph $G$ is the minimum cardinality of a resolving set of $G$. A resolving set with cardinality $\dim(G)$ is called a metric basis of $G$. We...

Resolving sets were originally designed to locate vertices of a graph one at a time. For the purpose of locating multiple vertices of the graph simultaneously, $\{\ell\}$-resolving sets were recently introduced. In this paper, we present new results regarding the $\{\ell\}$-resolving sets of a graph. In addition to proving general results, we consi...

Resolving sets were originally designed to locate vertices of a graph one at a time. For the purpose of locating multiple vertices of the graph simultaneously, {ℓ}-resolving sets were recently introduced. In this paper, we present new results regarding the {ℓ}-resolving sets of a graph. In addition to proving general results, we consider {2}-resolv...

Resolving sets are designed to locate an object in a network by measuring the distances to the object. However, if there are more than one object present in the network, this can lead to wrong conclusions. To overcome this problem, we introduce the concept of solid-resolving sets. In this paper, we study the structure and constructions of solid-res...