TY - JOUR
AU - Ponomarchuk, B.S.
PY - 2019/12/31
Y2 - 2024/05/19
TI - Metric dimension of metric transform and wreath product
JF - Carpathian Mathematical Publications
JA - Carpathian Math. Publ.
VL - 11
IS - 2
SE - Scientific articles
DO - 10.15330/cmp.11.2.418-421
UR - https://journals.pnu.edu.ua/index.php/cmp/article/view/2119
SP - 418-421
AB - <p>Let $(X,d)$ be a metric space. A non-empty subset $A$ of the set $X$ is called <em>resolving</em> set of the metric space $(X,d)$ if for two arbitrary not equal points $u,v$ from $X$ there exists an element $a$ from $A$, such that $d(u,a)
eq d(v,a)$. The smallest of cardinalities of resolving subsets of the set $X$ is called <em>the metric dimension</em> $md(X)$ of the metric space $(X,d)$.</p><p>In general, finding the metric dimension is an NP-hard problem. In this paper, metric dimension for metric transform and wreath product of metric spaces are provided. It is shown that the metric dimension of an arbitrary metric space is equal to the metric dimension of its metric transform.</p>
ER -