**Dorota Kuziak**

*Article*

Departamento de Estadística e Investigación Operativa, Universidad de Cádiz, 11003 Cádiz, Spain; dorota.kuziak@uca.es

Received: 12 July 2020; Accepted: 21 July 2020; Published: 2 August 2020

**Abstract:** A vertex *w* of a connected graph *G* strongly resolves two distinct vertices *u*, *v* ∈ *<sup>V</sup>*(*G*), if there is a shortest *u*, *w* path containing *v*, or a shortest *v*, *w* path containing *u*. A set *S* of vertices of *G* is a *strong resolving set* for *G* if every two distinct vertices of *G* are strongly resolved by a vertex of *S*. The smallest cardinality of a strong resolving set for *G* is called the *strong metric dimension* of *G*. To study the strong metric dimension of graphs, a very important role is played by a structure of graphs called the strong resolving graph In this work, we obtain the strong metric dimension of some families of cactus graphs, and along the way, we give several structural properties of the strong resolving graphs of the studied families of cactus graphs.

**Keywords:** strong resolving graph; strong metric dimension; strong resolving set; cactus graphs; unicyclic graphs

**MSC:** 05C12
