Some properties of the multiset dimension of graphs

The multiset dimension was introduced by Rinovia Simanjuntak et al. as a variation of metric dimension. In this problem, the representation of a vertex v with respect to a resolving set W is expressed as a multiset of distances between v and all vertices in W , including their multiplicities. The multiset dimension is defined to be the minimum cardinality of the resolving set. Clearly, this is at least the metric dimension of a graph. In this paper, we study the properties of the multiset dimension of graphs.