Results 11 to 20 of about 150,008 (260)
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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Maximal resolving sets in a graph
International Journal of Mathematics for IndustryLet G be a connected graph. A subset [Formula: see text] of [Formula: see text] is called a resolving set of G if the code of any vertex [Formula: see text] with respect to S is different from the code of any other vertex where code of u with respect to ...
V. Swaminathan, R. Sundareswaran
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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 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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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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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
Datchev, Kiril, Vasy, András
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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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On the Characterization of a Minimal Resolving Set for Power of Paths
Mathematics, 2022 For a simple connected graph G=(V,E), an ordered set W⊆V, is called a resolving set of G if for every pair of two distinct vertices u and v, there is an element w in W such that d(u,w)≠d(v,w).
Laxman Saha +4 more
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Application of Metric Dimensions to Minimize the Installation of Fire Sensors on The Rectorate Building of Pasifik Morotai University [PDF]
MATEC Web of Conferences, 2022 The metric dimension of the connected graph G for each 𝑣 𝜖 𝑉(𝐺) to the set W is . The set r (ν|W) = (d(ν, w1), d(ν,w2),…d(ν,wk) W is called the resolving set if every vertex u,v in G, if u ≠ ν , then r (u|W) ≠ r (ν|W) .
Parera Cicilya Orissa F. +3 more
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Bounds on the domination number and the metric dimension of co-normal product of graphs
Journal of Inequalities and Applications, 2018 In this paper, we establish bounds on the domination number and the metric dimension of the co-normal product graph GH $G_{H}$ of two simple graphs G and H in terms of parameters associated with G and H.
Imran Javaid +2 more
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