Results 11 to 20 of about 1,385,922 (245)
Metric dimension of fullerene graphs [PDF]
Electronic Journal of Graph Theory and Applications, 2019 A resolving set W is a set of vertices of a graph G(V, E) such that for every pair of distinct vertices u, v ∈ V(G), there exists a vertex w ∈ W satisfying d(u, w) ≠ d(v, w).
Shehnaz Akhter, Rashid Farooq
doaj +3 more sources
On the Metric Dimension of Infinite Graphs [PDF]
Electronic Notes in Discrete Mathematics, 2009 A set of vertices $S$ \emph{resolves} a graph $G$ if every vertex is uniquely determined by its vector of distances to the vertices in $S$. The \emph{metric dimension} of a graph $G$ is the minimum cardinality of a resolving set. In this paper we study the metric dimension of infinite graphs such that all its vertices have finite degree.
José Cáceres +4 more
core +8 more sources
Metric dimension of metric transform and wreath product
Karpatsʹkì Matematičnì Publìkacìï, 2019 Let $(X,d)$ be a metric space. A non-empty subset $A$ of the set $X$ is called resolving 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 $d(u,a) \neq d(v,a)$.
B.S. Ponomarchuk
doaj +2 more sources
Metric Mean Dimension and Mean Hausdorff Dimension Varying the Metric [PDF]
Qualitative Theory of Dynamical SystemsAbstractLet $$f:\mathbb {M}\rightarrow \mathbb {M}$$ f : M → M be a continuous map on a compact metric space $$\mathbb {M}$$ M equipped with a fixed metric d, and ...
Becker, Alex Jenaro +3 more
core +6 more sources
On the Complexity of Metric Dimension [PDF]
, 2012 The metric dimension of a graph G is the size of a smallest subset L ⊆ V(G) such that for any x,y ∈ V(G) there is a z ∈ L such that the graph distance between x and z differs from the graph distance between y and z. Even though this notion has been part of the literature for almost 40 years, the computational complexity of determining the metric ...
Josep Díaz +3 more
openaire +6 more sources
Metric Dimension for Random Graphs [PDF]
The Electronic Journal of Combinatorics, 2013 The metric dimension of a graph $G$ is the minimum number of vertices in a subset $S$ of the vertex set of $G$ such that all other vertices are uniquely determined by their distances to the vertices in $S$. In this paper we investigate the metric dimension of the random graph $G(n,p)$ for a wide range of probabilities $p=p(n)$.
Béla Bollobás +2 more
core +7 more sources
Metric Dimension Parameterized By Treewidth [PDF]
Algorithmica, 2021 AbstractA resolving set S of a graph G is a subset of its vertices such that no two vertices of G have the same distance vector to S. The Metric Dimension problem asks for a resolving set of minimum size, and in its decision form, a resolving set of size at most some specified integer.
Édouard Bonnet, Nidhi Purohit
openaire +8 more sources
On metric dimensions of hypercubes
Ars Mathematica Contemporanea, 2022 The metric (resp. edge metric or mixed metric) dimension of a graph $G$, is the cardinality of the smallest ordered set of vertices that uniquely recognizes all the pairs of distinct vertices (resp. edges, or vertices and edges) of $G$ by using a vector of distances to this set. In this note we show two unexpected results on hypercube graphs. First, we
Aleksander Kelenc +3 more
openaire +5 more sources
ON METRIC DIMENSION OF FUNCTIGRAPHS [PDF]
Discrete Mathematics, Algorithms and Applications, 2013 The metric dimension of a graph G, denoted by dim (G), is the minimum number of vertices such that each vertex is uniquely determined by its distances to the chosen vertices. Let G1and G2be disjoint copies of a graph G and let f : V(G1) → V(G2) be a function. Then a functigraphC(G, f) = (V, E) has the vertex set V = V(G1) ∪ V(G2) and the edge set E = E(
Linda Eroh, Cong X. Kang, Eunjeong Yi
openaire +3 more sources
Sequential Metric Dimension [PDF]
Algorithmica, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bensmail, Julien +4 more
openaire +6 more sources