Results 11 to 20 of about 855,405 (264)
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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Optimal Multi-Level Fault-Tolerant Resolving Sets of Circulant Graph C(n : 1, 2)
Mathematics, 2023 Let G=(V(G),E(G)) be a simple connected unweighted graph. A set R⊂V(G) is called a fault-tolerant resolving set with the tolerance level k if the cardinality of the set Sx,y={w∈R:d(w,x)≠d(w,y)} is at least k for every pair of distinct vertices x,y of G ...
Laxman Saha +4 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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Optimal Fault-Tolerant Resolving Set of Power Paths
Mathematics, 2023 In a simple connected undirected graph G, an ordered set R of vertices is called a resolving set if for every pair of distinct vertices u and v, there is a vertex w∈R such that d(u,w)≠d(v,w).
Laxman Saha +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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Semiclassical resolvent estimates at trapped sets [PDF]
Annales de l'Institut Fourier, 2012 We extend our recent results on propagation of semiclassical resolvent estimates through trapped sets when a priori polynomial resolvent bounds hold. Previously we obtained non-trapping estimates in trapping situations when the resolvent was sandwiched between cutoffs χ microlocally supported away from the trapping: ∥χR h (E+i0)χ∥=𝒪(h -1 ), a ...
Datchev, Kiril, Vasy, András
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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 $ $ of the distance it traveled.
Aronov, Boris +2 more
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The dominant metric dimension of graphs
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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On classes of neighborhood resolving sets of a graph
Electronic Journal of Graph Theory and Applications, 2018 Let G = (V, E) be a simple connected graph. A subset S of V is called a neighbourhood set of G if G = ⋃s ∈ S < N[s] > , where N[v] denotes the closed neighbourhood of the vertex v in G. Further for each ordered subset S = {s1, s2, ..., sk} of V and
B. Sooryanarayana, Suma A. S.
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On Resolvability- and Domination-Related Parameters of Complete Multipartite Graphs
Mathematics, 2022 Graphs of order n with fault-tolerant metric dimension n have recently been characterized.This paper points out an error in the proof of this characterization. We show that the complete multipartite graphs also have the fault-tolerant metric dimension n,
Sakander Hayat, Asad Khan, Yubin Zhong
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