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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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Dimensi Metrik Kuat Lokal Graf Hasil Operasi Kali Kartesian
Contemporary Mathematics and Applications (ConMathA), 2020 The strong local metric dimension is the development result of a strong metric dimension study, one of the study topics in graph theory. Some of graphs that have been discovered about strong local metric dimension are path graph, star graph, complete ...
Nurma Ariska Sutardji +2 more
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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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Edge Metric and Fault-Tolerant Edge Metric Dimension of Hollow Coronoid
Mathematics, 2021 Geometric arrangements of hexagons into six sides of benzenoids are known as coronoid systems. They are organic chemical structures by definition. Hollow coronoids are divided into two types: primitive and catacondensed coronoids.
Ali N. A. Koam +3 more
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Nonlocal Metric Dimension of Graphs
Bulletin of the Malaysian Mathematical Sciences Society, 2023 Nonlocal metric dimension ${\rm dim}_{\rm n\ell}(G)$ of a graph $G$ is introduced as the cardinality of a smallest nonlocal resolving set, that is, a set of vertices which resolves each pair of non-adjacent vertices of $G$. Graphs $G$ with ${\rm dim}_{\rm n\ell}(G) = 1$ or with ${\rm dim}_{\rm n\ell}(G) = n(G)-2$ are characterized.
Sandi Klavžar, Dorota Kuziak
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Metric Dimensions of Bicyclic Graphs
Mathematics, 2023 The distance d(va,vb) between two vertices of a simple connected graph G is the length of the shortest path between va and vb. Vertices va,vb of G are considered to be resolved by a vertex v if d(va,v)≠d(vb,v). An ordered set W={v1,v2,v3,…,vs}⊆V(G) is said to be a resolving set for G, if for any va,vb∈V(G),∃vi∈W∋d(va,vi)≠d(vb,vi). The representation of
Asad Khan +5 more
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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
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Fault-Tolerant Metric Dimension of Circulant Graphs
Mathematics, 2022 Let G be a connected graph with vertex set V(G) and d(u,v) be the distance between the vertices u and v. A set of vertices S={s1,s2,…,sk}⊂V(G) is called a resolving set for G if, for any two distinct vertices u,v∈V(G), there is a vertex si∈S such that d ...
Laxman Saha +4 more
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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 $p=p(n)$.
Bollobás, Béla +2 more
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On the Dominant Local Resolving Set of Vertex Amalgamation Graphs
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2023 Basically, the new topic of the dominant local metric dimension which be symbolized by Ddim_l (H) is a combination of two concepts in graph theory, they were called the local metric dimension and dominating set. There are some terms in this topic that is
Reni Umilasari +3 more
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