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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 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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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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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 star fan graph [PDF]
Scientific ReportsEvery node in a network is said to be resolved if it can be uniquely identified by a vector of distances to a specific set of nodes. The metric dimension is equivalent to the least possible cardinal number of a resolving set.
S. Prabhu +2 more
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Graphs of Neighborhood Metric Dimension Two
Journal of Mathematical and Fundamental Sciences, 2021 A subset of vertices of a simple connected graph is a neighborhood set (n-set) of G if G is the union of subgraphs of G induced by the closed neighbors of elements in S. Further, a set S is a resolving set of G if for each pair of distinct vertices x,y
Badekara Sooryanarayana +1 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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On Mixed Metric Dimension of Rotationally Symmetric Graphs
IEEE Access, 2020 A vertex u ∈ V(G) resolves (distinguish or recognize) two elements (vertices or edges) v, w ∈ E(G)UV(G) if dG(u, v) ≠ dG(u, w) . A subset Lm of vertices in a connected graph G is called a mixed metric generator for G if every two ...
Hassan Raza, Jia-Bao Liu, Shaojian Qu
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Remarks on the Vertex and the Edge Metric Dimension of 2-Connected Graphs
Mathematics, 2022 The vertex (respectively edge) metric dimension of a graph G is the size of a smallest vertex set in G, which distinguishes all pairs of vertices (respectively edges) in G, and it is denoted by dim(G) (respectively edim(G)). The upper bounds dim(G)≤2c(G)−
Martin Knor +2 more
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On Mixed Metric Dimension of Some Path Related Graphs
IEEE Access, 2020 A vertex $k\in V_{G}$ determined two elements (vertices or edges) $\ell,m \in V_{G}\cup E_{G}$ , if $d_{G}(k,\ell)\neq d_{G}(k,m)$ . A set $R_ {\text {m}}$ of vertices in a graph $G$ is a mixed metric generator for $G$ , if two distinct elements
Hassan Raza, Ying Ji, Shaojian Qu
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