Some properties of the multiset dimension of graphs

Novi H. Bong, Yuqing Lin

Abstract


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. 


Keywords


multiset dimension, distance metric dimension, upper bound

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DOI: http://dx.doi.org/10.5614/ejgta.2021.9.1.19

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