Jaan Allikvere

The Multiset Dimension of Graphs: Extremal Values and King Grids

We present three results on the multiset dimension of graphs, resolving one conjecture and two open questions from the literature. First, we disprove the conjecture of Simanjuntak, Siagian and Vetr\'ik (2017) that every graph $G$ of order $n(G)$ with finite multiset dimension satisfies $\dim_m(G) \le n(G)-1$: an exhaus...