Note on metric-dependent dimension functions
نویسندگان
چکیده
منابع مشابه
Note on Metric Dimension
The metric dimension of a compact metric space is defined here as the order of growth of the exponential metric entropy of the space. The metric dimension depends on the metric, but is always bounded below by the topological dimension. Moreover, there is always an equivalent metric in which the metric and topological dimensions agree. This result may be used to define the topological dimension ...
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A set $Wsubseteq V(G)$ is called a resolving set for $G$, if for each two distinct vertices $u,vin V(G)$ there exists $win W$ such that $d(u,w)neq d(v,w)$, where $d(x,y)$ is the distance between the vertices $x$ and $y$. The minimum cardinality of a resolving set for $G$ is called the metric dimension of $G$, and denoted by $dim(G)$. In this paper, it is proved that in a connected graph $...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1967
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-61-1-83-89