Results 31 to 40 of about 60,505 (275)
Double edge resolving set and exchange property for nanosheet structure
HeliyonThe exploration of edge metric dimension and its applications has been an ongoing discussion, particularly in the context of nanosheet graphs formed from the octagonal grid. Edge metric dimension is a concept that involves uniquely identifying the entire
Ali N.A. Koam +4 more
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Unicyclic graphs with non-isolated resolving number $2$ [PDF]
Transactions on Combinatorics, 2023 Let $G$ be a connected graph and $W=\{w_1, w_2,\ldots,w_k\}$ be an ordered subset of vertices of $G$. For any vertex $v$ of $G$, the ordered $k$-vector $$r(v|W)=(d(v,w_1), d(v,w_2),\ldots,d(v,w_k))$$ is called the metric representation of $v$ with ...
Mohsen Jannesari
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Resolving SINR Queries in a Dynamic Setting [PDF]
SIAM Journal on Computing, 2020 We consider a set of transmitters broadcasting simultaneously on the same frequency under the SINR model. Transmission power may vary from one transmitter to another, and a transmitter's signal strength at a given point is modeled by the transmitter's power divided by some constant power $α$ of the distance it traveled.
Boris Aronov +2 more
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Resolving sets of vertices with the minimum size in graphs [PDF]
ریاضی و جامعه, 2023 Suppose that $G$ is a simple connected graph with vertex set $V(G)$ and edge set $E(G)$. A subset $S=\{s_1, s_2,\ldots , s_l \}$ of vertices of graph $G$ is called a doubly resolving set of $G$, if for any distinct vertices $u$ and $v$ in $G$ there are ...
Ali Zafari, Nader Habibi, Saeid Alikhani
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Resolving Sets and Semi-Resolving Sets in Finite Projective Planes [PDF]
The Electronic Journal of Combinatorics, 2012 In a graph $\Gamma=(V,E)$ a vertex $v$ is resolved by a vertex-set $S=\{v_1,\ldots,v_n\}$ if its (ordered) distance list with respect to $S$, $(d(v,v_1),\ldots,d(v,v_n))$, is unique. A set $A\subset V$ is resolved by $S$ if all its elements are resolved by $S$. $S$ is a resolving set in $\Gamma$ if it resolves $V$.
Héger, Tamás, Takáts, Marcella
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The Edge Version of Metric Dimension for the Family of Circulant Graphs Cₙ(1, 2)
IEEE Access, 2021 Graph theory is widely used to analyze the structure models in chemistry, biology, computer science, operations research and sociology. Molecular bonds, species movement between regions, development of computer algorithms, shortest spanning trees in ...
Junya Lv +3 more
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Computing the partition dimension of certain families of Toeplitz graph
Frontiers in Computational Neuroscience, 2022 Let G = (V(G), E(G)) be a graph with no loops, numerous edges, and only one component, which is made up of the vertex set V(G) and the edge set E(G). The distance d(u, v) between two vertices u, v that belong to the vertex set of H is the shortest path ...
Ricai Luo +5 more
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Study of Convexo-Symmetric Networks via Fractional Dimensions
IEEE Access, 2022 For having an in-depth study and analysis of various network’s structural properties such as interconnection, extensibility, availability, centralization, vulnerability and reliability, we require distance based graph theoretic parameters ...
Muhammad Kamran Aslam +3 more
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Certain Varieties of Resolving Sets of A Graph [PDF]
Journal of the Indonesian Mathematical Society, 2021 Let G=(V,E) be a simple connected graph. For each ordered subset S={s_1,s_2,...,s_k} of V and a vertex u in V, we associate a vector Gamma(u/S)=(d(u,s_1),d(u,s_2),...,d(u,s_k)) with respect to S, where d(u,v) denote the distance between u and v in G. A subset S is said to be resolving set of G if Gamma(u/S) not equal to Gamma(v/S) for all u, v in V-S ...
Sooryanarayana, Badekara +2 more
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Resolving sets tolerant to failures in three-dimensional grids
, 2021 An ordered set $S$ of vertices of a graph $G$ is a resolving set for $G$ 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.
Salorio, María José Souto +6 more
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