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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 Dimension Threshold of Graphs
Journal of Mathematics, 2022 Let G be a connected graph. A subset S of vertices of G is said to be a resolving set of G, if for any two vertices u and v of G there is at least a member w of S such that du,w≠dv,w.
Meysam Korivand +2 more
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Strong metric dimension: A survey [PDF]
Yugoslav Journal of Operations Research, 2014 The strong metric dimension has been a subject of considerable amount of research in recent years. This survey describes the related development by bringing together theoretical results and computational approaches, and places the recent results
Kratica Jozef +3 more
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Spread: a measure of the size of metric spaces [PDF]
, 2014 Motivated by Leinster-Cobbold measures of biodiversity, the notion of the spread of a finite metric space is introduced. This is related to Leinster's magnitude of a metric space.
Willerton, Simon
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On the metric dimension of Cayley graphs
AKCE International Journal of Graphs and Combinatorics, 2022 In this paper, we investigate the metric dimension, local metric dimension and edge metric dimension for some (generalized) Cayley graphs.
Afsaneh Rezaei +2 more
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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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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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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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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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Axisymmetric metrics in arbitrary dimensions [PDF]
Classical and Quantum Gravity, 2003 We consider axially symmetric static metrics in arbitrary dimension, both with and without a cosmological constant. The most obvious such solutions have an SO(n) group of Killing vectors representing the axial symmetry, although one can also consider abelian groups which represent a flat `internal space'.
Charmousis, Christos, Gregory, Ruth
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