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 ...
متن کاملThe metric dimension and girth of graphs
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 $...
متن کاملOn dimension of a special subalgebra of derivations of nilpotent Lie algebras
Let $L$ be a Lie algebra, $mathrm{Der}(L)$ be the set of all derivations of $L$ and $mathrm{Der}_c(L)$ denote the set of all derivations $alphainmathrm{Der}(L)$ for which $alpha(x)in [x,L]:={[x,y]vert yin L}$ for all $xin L$. We obtain an upper bound for dimension of $mathrm{Der}_c(L)$ of the finite dimensional nilpotent Lie algebra $L$ over algebraically closed fields. Also, we classi...
متن کاملOn the metric dimension and fractional metric dimension for hierarchical product of graphs
A set of vertices W resolves a graph G if every vertex of G is uniquely determined by its vector of distances to the vertices in W . The metric dimension for G, denoted by dim(G), is the minimum cardinality of a resolving set of G. In order to study the metric dimension for the hierarchical product G2 2 uG1 1 of two rooted graphs G2 2 and G u1 1 , we first introduce a new parameter, the rooted ...
متن کاملthe metric dimension and girth of graphs
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: 1964
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-55-2-181-194