منابع مشابه
On optimal approximability results for computing the strong metric dimension
In this short note, we observe that the problem of computing the strong metric dimension of a graph can be reduced to the problem of computing a minimum node cover of a transformed graph within an additive logarithmic factor. This implies both a 2-approximation algorithm and a (2−ε)-inapproximability for the problem of computing the strong metric dimension of a graph.
متن کاملOn the Strong Metric Dimension of Cartesian Sum Graphs
A vertex w of a connected graph G strongly resolves two vertices u, v ∈ V (G), if there exists some shortest u−w path containing v or some shortest v−w path containing u. A set S of vertices is a strong metric generator for G if every pair of vertices of G is strongly resolved by some vertex of S. The smallest cardinality of a strong metric generator for G is called the strong metric 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 کاملNote 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 کاملConditional Dimension in Metric Spaces: A Natural Metric-Space Counterpart of Kolmogorov-Complexity-Based Mutual Dimension
It is known that dimension of a set in a metric space can be characterized in information-related terms – in particular, in terms of Kolmogorov complexity of different points from this set. The notion of Kolmogorov complexity K(x) – the shortest length of a program that generates a sequence x – can be naturally generalized to conditional Kolmogorov complexity K(x : y) – the shortest length of a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: YUJOR
سال: 2014
ISSN: 0354-0243,1820-743X
DOI: 10.2298/yjor130520042k