Results 11 to 20 of about 888,398 (240)
Metric mean dimension and mean Hausdorff dimension varying the metric [PDF]
arXivLet $f: M\rightarrow M$ be a continuous map on a compact metric space $M$ equipped with a fixed metric $d$, and let $\tau$ be the topology on $M$ induced by $d$. First, we will establish some fundamental properties of the mean Hausdorff dimension. Furthermore, it is important to note that the metric mean dimension and mean Hausdorff dimension depend on
Muentes Acevedo, Jeovanny de Jesus +3 more
arxiv +4 more sources
Metric dimension of Andrásfai graphs [PDF]
Opuscula Mathematica, 2019 A set \(W\subseteq V(G)\) is called a resolving set, if for each pair of distinct vertices \(u,v\in V(G)\) there exists \(t\in W\) such that \(d(u,t)\neq d(v,t)\), where \(d(x,y)\) is the distance between vertices \(x\) and \(y\).
S. Batool Pejman +2 more
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Computation of mixed resolvability for a circular ladder and its unbounded nature. [PDF]
PLoS ONELet Γ = Γ(V ,E) be a simple, planar, connected, and undirected graph. The article primarily concentrates on a category of planar graphs, detailing the explicit identification of each member within this graph family. Within the domain of graph theory, the
Sunny Kumar Sharma +4 more
doaj +2 more sources
Metric dimension and equivalent metrics [PDF]
Fundamenta Mathematicae, 1968 J. H. Roberts, F. Slaughert
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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 +2 more
openaire +7 more sources
Graphs with the edge metric dimension smaller than the metric dimension [PDF]
Applied Mathematics and Computation, 2021 11 ...
Martin Knor +4 more
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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
Kelenc, Aleksander +3 more
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Sequential Metric Dimension [PDF]
Algorithmica, 2018 Seager introduced the following game in 2013. An invisible and immobile target is hidden at some vertex of a graph $G$. Every step, one vertex $v$ of $G$ can be probed which results in the knowledge of the distance between $v$ and the target. The objective of the game is to minimize the number of steps needed to locate the target, wherever it is.
Bensmail, Julien +4 more
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Graphs of Neighborhood Metric Dimension Two
Journal of Mathematical and Fundamental Sciences, 2021 A subset of vertices of a simple connected graph is a neighborhood set (n-set) of G if G is the union of subgraphs of G induced by the closed neighbors of elements in S. Further, a set S is a resolving set of G if for each pair of distinct vertices x,y
Badekara Sooryanarayana +1 more
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