Further results on the mixed metric dimension of graphs

Let G be a graph with vertex set V(G) and edge set E(G). The mixed metric dimension of a connected graph G, denoted by dimm(G), is the minimum cardinality of a subset S C V(G) such that for any two u, v E V(G)UE(G), there exists w E S so that the distance between wand u is not equal to the distance between wand v. In this paper, we present further results on the mixed metric dimension. First, we give a sharp upper bound on the mixed metric dimension for a graph in terms of the number of cut vertices of this graph. Second, we compare the mixed metric dimension with geodesic transversal number for trees, unicyclic graphs and block graphs. Finally, we provide some new results about a conjecture, due to Sedlar and & Scaron;krekovski (Sedlar and & Scaron;krekovski, 2021), on the mixed metric dimension. (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.