Results 31 to 40 of about 8,830,736 (317)
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 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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Determining Sets, Resolving Sets, and the Exchange Property [PDF]
Graphs and Combinatorics, 2009 A subset U of vertices of a graph G is called a determining set if every automorphism of G is uniquely determined by its action on the vertices of U. A subset W is called a resolving set if every vertex in G is uniquely determined by its distances to the vertices of W. Determining (resolving) sets are said to have the exchange property in G if whenever
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Resolvents, integral equations, limit sets [PDF]
Mathematica Bohemica, 2010 Summary: We study a linear integral equation \(x(t)=a(t)-\int ^t_0 C(t,s) x(s)\, \text{d}s\), its resolvent equation \(R(t,s)=C(t,s)-\int ^t_s C(t,u)R(u,s)\,\text{d}u\), the variation of parameters formula \(x(t)=a(t)-\int ^t_0 R(t,s)a(s)\, \text{d}s\) and a perturbed equation.
Burton, T. A., Dwiggins, D. P.
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Resolving sets for Johnson and Kneser graphs [PDF]
, 2012 A set of vertices $S$ in a graph $G$ is a {\em resolving set} for $G$ if, for any two vertices $u,v$, there exists $x\in S$ such that the distances $d(u,x) \neq d(v,x)$.
Alberto Márquez +37 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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Benchmarking photon number resolving detectors. [PDF]
Optics Express, 2020 Photon number resolving detectors are the ultimate measurement of quantum optics, which is the reason why developing the technology is getting significant attention in recent years.
Jan Provazn'ik +3 more
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Error-correcting codes from k-resolving sets
Discussiones Mathematicae Graph Theory, 2019 13 pages, 2 ...
Bailey, Robert F. +1 more
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Resolving Independent Dominating Set pada Graf Bunga, Graf Gear, dan Graf Bunga Matahari
Contemporary Mathematics and Applications (ConMathA), 2023 Resolving independent dominating set is the development of metric dimension and independent dominating set. Resolving independent dominating sets is a concept which discusses about determining the minimum vertex on a graph provided that the vertex that ...
Rafiantika Megahniah Prihandini +4 more
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