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Metric dimension and edge metric dimension of windmill graphs
AIMS Mathematics, 2021 Graph invariants provide an amazing tool to analyze the abstract structures of graphs. Metric dimension and edge metric dimension as graph invariants have numerous applications, among them are robot navigation, pharmaceutical chemistry, etc.
Pradeep Singh +3 more
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ON METRIC DIMENSION OF FUNCTIGRAPHS [PDF]
Discrete Mathematics, Algorithms and Applications, 2013 The metric dimension of a graph G, denoted by dim (G), is the minimum number of vertices such that each vertex is uniquely determined by its distances to the chosen vertices. Let G1and G2be disjoint copies of a graph G and let f : V(G1) → V(G2) be a function. Then a functigraphC(G, f) = (V, E) has the vertex set V = V(G1) ∪ V(G2) and the edge set E = E(
Eroh, Linda, Kang, Cong X., Yi, Eunjeong
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Metric and fault-tolerant metric dimension for GeSbTe superlattice chemical structure [PDF]
PLoS ONE, 2023 The concept of metric dimension has many applications, including optimizing sensor placement in networks and identifying influential persons in social networks, which aids in effective resource allocation and focused interventions; finding the source of ...
Liu Liqin +4 more
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The Metric Dimension and Local Metric Dimension of Relative Prime Graph [PDF]
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2020 This study aims to determine the value of metric dimensions and local metric dimensions of relative prime graphs formed from modulo integer rings, namely . As a vertex set is and if and are relatively prime.
Inna Kuswandari +2 more
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Optimizing emergency response services in urban areas through the fault-tolerant metric dimension of hexagonal nanosheet [PDF]
Scientific ReportsIn this work, we find the fault-tolerant metric dimension of a hexagonal nanosheet. This concept ensures robust identity of vertices inside a graph, even in situations in which a few resolving vertices fail.
Yaoyao Tu +5 more
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Fault-Tolerant Metric Dimension of Interconnection Networks [PDF]
IEEE Access, 2020 A fixed interconnection parallel architecture is characterized by a graph, with vertices corresponding to processing nodes and edges representing communication links.
Sakander Hayat +4 more
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The dominant metric dimension of graphs [PDF]
Heliyon, 2020 The G be a connected graph with vertex set V(G) and edge set E(G). A subset S⊆V(G) is called a dominating set of G if for every vertex x in V(G)∖S, there exists at least one vertex u in S such that x is adjacent to u.
Liliek Susilowati +4 more
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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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Metric, edge-metric, mixed-metric, and fault-tolerant metric dimensions of geometric networks with potential applications [PDF]
Scientific ReportsResolvability parameters of graphs are widely applicable in fields like computer science, chemistry, and geography. Many of these parameters, such as the metric dimension, are computationally hard to determine. This paper focuses on Möbius-type geometric
Sakander Hayat +6 more
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Metric Dimension of Amalgamation of Graphs [PDF]
, 2013 A set of vertices $S$ resolves a graph $G$ if every vertex is uniquely determined by its vector of distances to the vertices in $S$. The metric dimension of $G$ is the minimum cardinality of a resolving set of $G$.
Rinovia Simanjuntak +2 more
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