During the last two decades, there has been a growing interest in locating extensive facilities, such as paths, on networks. In this paper we study the median path problem without restrictions on its length on the class of connected outerplanar graphs with equal weights assigned to the edges and nonnegative weights associated to the vertices. We provide a O(kn) time algorithm, where n is the nu...

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 metric-locationdomination number. In this paper, we undertake a study that, in general graphs and specific families, relates metric-locating-dominating sets to other special sets: ...

In this article, we study locating-dominating codes in binary Hamming spaces $$\mathbb {F}^n$$ . Locating-dominating have been widely studied since their introduction 1980s by Slater and Rall. They are dominating sets suitable for distinguishing vertices graphs. Dominating as well multiple articles. Previously, Honkala et al. (Discret Math Theor Comput Sci 6(2):265, 2004) presented a lower boun...

A dominating set S of a graph G is a locating-dominating-set, 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 are called LDcodes and the cardinality of an LD-code is the location-domination number, λ(G). An LD-set S of a graph G is global if it is an LD-set for both G and its complem...