The metric dimension of a graph is the smallest number of nodes required to identify all
other nodes uniquely based on shortest path distances. Applications of metric dimension …

We consider the problems of finding optimal identifying codes,(open) locating-dominating
sets and resolving sets (denoted Identifying Code,(Open) Open Locating-Dominating Set …

We investigate fine-grained algorithmic aspects of identification problems in graphs and set
systems, with a focus on Locating-Dominating Set and Test Cover. We prove, among other …

The notion of resolving sets in a graph was introduced by Slater Proceedings of the Sixth
Southeastern Conference on Combinatorics, Graph Theory, and Computing, Util. Math …

We give essentially tight bounds for, ν (d, k), the maximum number of distinct
neighbourhoods on a set X of k vertices in a graph with twin-width at most d. Using the …

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 …

Let G be a graph with vertex set V (G), and let d (x, y) denote the length of a shortest path
between nodes x and y in G. For a positive integer k and for distinct x, y∈ V (G), let dk (x, y) …

An identifying code of a graph is a subset of its vertices such that every vertex of the graph is
uniquely identified by the set of its neighbors within the code. We show a dichotomy for the …

An identifying code is a subset of vertices of a graph with the property that each vertex is
uniquely determined (identified) by its nonempty neighbourhood within the identifying code …

A graph $ G=(V, E) $ with geodesic distance $ d (\cdot,\cdot) $ is said to be resolved by a
non-empty subset $ R $ of its vertices when, for all vertices $ u $ and $ v $, if $ d (u, r)= d (v …