@article{Alfarisi_Lin_Ryan_Dafik_Agustin_2020, title={A Note on Multiset Dimension and Local Multiset Dimension of Graphs}, volume={8}, url={http://iapress.org/index.php/soic/article/view/727}, DOI={10.19139/soic-2310-5070-727}, abstractNote={<p>All graphs in this paper are nontrivial and connected simple graphs. For a set W = {s1,s2,...,sk} of vertices<br>of G, the multiset representation of a vertex v of G with respect to W is r(v|W) = {d(v,s1),d(v,s2),...,d(v,sk)} where<br>d(v,si) is the distance between of v and si. If the representation r(v|W)̸=&nbsp;r(u|W) for every pair of vertices u,v of a graph G, the W is called the resolving set of G, and the cardinality of a minimum resolving set is called the multiset dimension, denoted by md(G). A set W is a local resolving set of G if r(v|W) ̸= r(u|W) for every pair of adjacent vertices u,v of a graph G. The cardinality of a minimum local resolving set W is called local multiset dimension, denoted by µ<sub>l</sub>(G). In our paper, we discuss the relationship between the multiset dimension and local multiset dimension of graphs and establish bounds of local multiset dimension for some families of graph.</p&gt;}, number={4}, journal={Statistics, Optimization & Information Computing}, author={Alfarisi, Ridho and Lin, Yuqing and Ryan, Joe and Dafik, Dafik and Agustin, Ika Hesti}, year={2020}, month={Sep.}, pages={890-901} }