Some properties of the multiset dimension of graphs

• Published in: Electronic Journal of Graph Theory and Applications
• Main Authors: Novi H. Bong, Yuqing Lin
• Format: Article
• Language: English
• Published: Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia 2021-04-01
• Subjects: multiset dimension, distance metric dimension, upper bound
• Online Access: https://www.ejgta.org/index.php/ejgta/article/view/1047
• ISSN: 2338-2287

<div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p class="p1">The multiset dimension was introduced by Rinovia Simanjuntak et al. as a variation of metric dimension. In this problem, the representation of a vertex <em>v</em> with respect to a resolving set <em>W</em> is expressed as a multiset of distances between <em>v</em> and all vertices in <em>W</em>, 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.<span class="Apple-converted-space"> </span></p></div></div></div>