\(l\)-clique metric dimension of graphs
In this paper, the well-studied concepts of the metric dimension and the edge metric dimension of graphs are extended to the \(l\)-clique metric dimension. The goal is to find the smallest ordered set of vertices such that all \(l\)-cliques are resolved by the set. The case \(l = 1\) is thus the metric dimension and the case \(l = 2\) is the edge metric dimension. In the core of the paper, the \(l\)-metric dimension is studied on generalized join graphs (more commonly referred to as generalized lexicographic products), certain graphs derived from commutative rings, and corona products. NP-completeness of the problem is also proved for each \(l\ge 3\) and an integer linear programming model for its solution is presented.
scientific article; zbMATH DE number 7610153
scientific article