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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 $p=p(n)$.
Béla Bollobás +2 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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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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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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Computing dominant metric dimensions of certain connected networks
HeliyonIn the studies of the connected networks, metric dimension being a distance-based parameter got much more attention of the researches due to its wide range of applications in different areas of chemistry and computer science. At present its various types
Imtiaz Ali, Muhammad Javaid, Yilun Shang
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IEEE AccessIn the aircraft sector, honeycomb composite materials are frequently employed. Recent research has demonstrated the benefits of honeycomb structures in applications involving nanohole arrays in anodized alumina, micro-porous arrays in polymer thin films,
Sidra Bukhari +3 more
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Metric dimension and edge metric dimension of unicyclic graphs
, 2021 The metric (resp. edge metric) dimension of a simple connected graph $G$, denoted by dim$(G)$ (resp. edim$(G)$), is the cardinality of a smallest vertex subset $S\subseteq V(G)$ for which every two distinct vertices (resp. edges) in $G$ have distinct distances to a vertex of $S$.
Zhu, Enqiang +2 more
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Pediatric Blood &Cancer, EarlyView.ABSTRACT Background Cerebellar ataxia after pediatric brain tumor treatment can cause persistent gait, balance, and speech impairment, yet no established rehabilitation strategy exists. Somato‐cognitive coordination therapy (SCCT) is a virtual reality–guided intervention designed to promote sensorimotor integration through visually constrained reaching
Masanobu Takeuchi +10 more
wiley +1 more source
Double resolvability parameters of fosmidomycin anti-malaria drug and exchange property
HeliyonThe practical and theoretical significance of the resolvability parameter makes it an important factor, particularly in the context of network analysis.
Rashad Ismail +3 more
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Metric dimension of fullerene graphs
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
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