Results 31 to 40 of about 238,609 (287)
European Journal of Pure and Applied MathematicsWhen there is a difference in the distance between two vertices in a simple linked graph, then a vertex $x$ resolves both $u$ and $v$. If at least one vertex in $S$ distinguishes each pair of distinct vertices in $G$, then a set $S$ of vertices in $G$ is
Waseem Abbas +4 more
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Edge Metric Dimension of Some Generalized Petersen Graphs [PDF]
Results in Mathematics, 2018 The edge metric dimension problem was recently introduced, which initiated the study of its mathematical properties. The theoretical properties of the edge metric representations and the edge metric dimension of generalized Petersen graphs GP(n, k) are ...
V. Filipovic +2 more
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Exploring metric dimension of nanosheets, nanotubes, and nanotori of SiO2. [PDF]
PLoS ONEThis work investigates the metric dimension (MD) and edge metric dimension (EMD) of SiO2 nanostructures, specifically nanosheets, nanotubes, and nanotorii.
Umar Farooq +4 more
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On the edge metric dimension of some classes of cacti
AIMS MathematicsThe cactus graph has many practical applications, particularly in radio communication systems. Let $ G = (V, E) $ be a finite, undirected, and simple connected graph, then the edge metric dimension of $ G $ is the minimum cardinality of the edge metric ...
Lyimo Sygbert Mhagama +2 more
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On metric dimension of edge comb product of vertex-transitive graphs [PDF]
Transactions on CombinatoricsSuppose finite graph $G$ is simple, undirected and connected. If $W$ is an ordered set of the vertices such that $|W| = k$, the representation of a vertex $v$ is an ordered $k$-tuple consisting distances of vertex $v$ with every vertices in $W$. The set $
Tita Maryati +3 more
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A remark on the metric dimension in Riemannian manifolds of constant curvature [PDF]
AUT Journal of Mathematics and ComputingWe compute the metric dimension of Riemannian manifolds of constant curvature. We define the edge weghited metric dimension of the geodesic graphs in Riemannian manifolds and we show that each complete geodesic graph $G=(V,E)$ embedded in a Riemannian ...
Shiva Heidarkhani Gilani +2 more
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Edge metric dimension of some classes of circulant graphs
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020 Let G = (V (G), E(G)) be a connected graph and x, y ∈ V (G), d(x, y) = min{ length of x − y path } and for e ∈ E(G), d(x, e) = min{d(x, a), d(x, b)}, where e = ab. A vertex x distinguishes two edges e1 and e2, if d(e1, x) ≠ d(e2, x). Let WE = {w1, w2, . .
Ahsan Muhammad +2 more
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Edge Metric Dimension of Silicate Networks [PDF]
Metric dimension is an essential parameter in graph theory that aids in addressing issues pertaining to information retrieval, localization, network design, and chemistry through the identification of the least possible number of elements necessary to identify the distances between vertices in a graph uniquely. A variant of metric dimension, called the
Prabhu, S., Jenifer Janany, T
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Edge based metric dimension of various coffee compounds.
PLoS ONEAn important dietary source of physiologically active compounds, coffee also contains phenolic acids, diterpenes, and caffeine. According to a certain study, some coffee secondary metabolites may advantageously modify a number of anti-cancer defense ...
Ali Ahmad +4 more
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Vertex and edge metric dimensions of cacti
Discrete Applied Mathematics, 2022 In a graph G; a vertex (resp. an edge) metric generator is a set of vertices S such that any pair of vertices (resp. edges) from G is distinguished by at least one vertex from S: The cardinality of a smallest vertex (resp. edge) metric generator is the vertex (resp. edge) metric dimension of G: In [19] we determined the vertex (resp.
Jelena Sedlar, Riste Skrekovski
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