Metric Dimension and Exchange Property for Resolving Sets in Rotationally-Symmetric Graphs
نویسندگان
چکیده
منابع مشابه
On the metric dimension of rotationally-symmetric convex polytopes∗
Metric dimension is a generalization of affine dimension to arbitrary metric spaces (provided a resolving set exists). Let F be a family of connected graphs Gn : F = (Gn)n ≥ 1 depending on n as follows: the order |V (G)| = φ(n) and lim n→∞ φ(n) = ∞. If there exists a constant C > 0 such that dim(Gn) ≤ C for every n ≥ 1 then we shall say that F has bounded metric dimension, otherwise F has unbou...
متن کاملDetermining Sets, Resolving Sets, and the Exchange Property
A subset U of vertices of a graph G is called a determining set if every automorphism of G is uniquely determined by its action on the vertices of U . A subset W is called a resolving set if every vertex in G is uniquely determined by its distances to the vertices of W . Determining (resolving) sets are said to have the exchange property in G if whenever S and R are minimal determining (resolvi...
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 کاملMinimal Doubly Resolving Sets and the Strong Metric Dimension of Hamming Graphs
The metric dimension problem, introduced independently by Slater [22] and Harary [8], has been widely investigated [1,3,5-7,9-13]. It arises in many diverse areas including network discovery and verification [2], geographical routing protocols [18], the robot navigation, connected joints in graphs, chemistry, etc. Given a simple connected undirected graph G = (VG,EG), where VG = {1, 2, ..., n},...
متن کاملMetric Dimension and R-Sets of Connected Graphs
The R-set relative to a pair of distinct vertices of a connected graph G is the set of vertices whose distances to these vertices are distinct. This paper deduces some properties of R-sets of connected graphs. It is shown that for a connected graph G of order n and diameter 2 the number of R-sets equal to V (G) is bounded above by n2/4 . It is conjectured that this bound holds for every connect...
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: Applied Mathematics & Information Sciences
سال: 2014
ISSN: 1935-0090,2325-0399
DOI: 10.12785/amis/080422