Some properties of the multiset dimension of graphs

Novi H. Bong, Yuqing Lin


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. 


multiset dimension, distance metric dimension, upper bound

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S. Akhter and R. Farooq, Metric dimension of fullerene graphs, Electron. J. Graph Theory Appl., 7 (1) (2019), 91–103.

G. Chartrand, L. Eroh, M.A. Johnson, and O.R. Oellermann, Resolvability in graphs and metric dimension of a graph, Discrete Appl. Math. 105 (2000), 99–113.

C. Grigorious, P. Manuel, M. Miller, B. Rajan, and S. Stephen, On the metric dimension of circulant and Harary graphs, Appl. Math. Comput. 248 (2014), 47–54.

F. Harary and R.A. Melter, On the metric dimension of a graph, Ars Combin. 2 (1976), 191–195.

A. Seb¨o and E. Tannier, On metric generators of graphs, Math. Oper. Res. 29 (2) (2004), 383–393.

R. Simanjuntak, T. Vetrık, and P. B. Mulia, The Multiset Dimension of Graphs, submitted,

P. J. Slater, Leaves of trees, Congr. Numer. 14 (1975), 549–559.


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