Results 21 to 30 of about 654,066 (314)
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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Study of modified prism networks via fractional metric dimension
AIMS Mathematics, 2023 For a connected network $ \Gamma $, the distance between any two vertices is the length of the shortest path between them. A vertex $ c $ in a connected network is said to resolve an edge $ e $ if the distances of $ c $ from its endpoints are unequal ...
Ahmed Alamer +2 more
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Graphs with mixed metric dimension three and related algorithms
AIMS Mathematics, 2023 Let $ G = (V, E) $ be a simple connected graph. A vertex $ x\in V(G) $ resolves the elements $ u, v\in E(G)\cup V(G) $ if $ d_G(x, u)\neq d_G(x, v) $.
Dalal Awadh Alrowaili +3 more
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Metric and Fault-Tolerant Metric Dimension of Hollow Coronoid
IEEE Access, 2021 Coronoid systems actually arrangements of hexagons into six sides of benzenoids. By nature, it is an organic chemical structure. Hollow coronoids are primitive and catacondensed coronoids. It is also known as polycyclic conjugated hydrocarbons.
Ali N. A. Koam +3 more
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Dimension of metric spaces [PDF]
Fundamenta Mathematicae, 1956 It is to be shown that a metric space has dimension ≤ n if and only if there exists a sequence {{ai} of locally finite open coverings, each of order ≤ n, with mesh tending to zero as i→∞, such that (a) the closure of each member of ai+1 is contained in some member of ai+1 is contained in some member of ai.
Witold Hurewicz, C. H. Dowker
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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.
Cáceres, José +4 more
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Study of Convexo-Symmetric Networks via Fractional Dimensions
IEEE Access, 2022 For having an in-depth study and analysis of various network’s structural properties such as interconnection, extensibility, availability, centralization, vulnerability and reliability, we require distance based graph theoretic parameters ...
Muhammad Kamran Aslam +3 more
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γ-Metrics in higher dimensions
Nuclear Physics B, 2022 9 pages, 1 ...
Hajibarat, Arash +2 more
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Note on Metric Dimension [PDF]
Proceedings of the American Mathematical Society, 1970 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.
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On Constant Metric Dimension of Some Generalized Convex Polytopes
Journal of Mathematics, 2021 Metric dimension is the extraction of the affine dimension (obtained from Euclidean space Ed) to the arbitrary metric space. A family ℱ=Gn of connected graphs with n≥3 is a family of constant metric dimension if dimG=k (some constant) for all graphs in ...
Xuewu Zuo +5 more
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