Results 21 to 30 of about 855,405 (264)

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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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, Mithun Basak, Kalishankar Tiwary, Kinkar Chandra Das, Yilun Shang   +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., Salmin Munazat, Bustan Ariestha Widyastuty, Mahmud Rauman   +3 more
doaj   +1 more source

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, Antonio González, Babai, Babai, Bailey, Bailey, Batten, Biggs, Blumenthal, Boutin, Brouwer, Cameron, Cameron, Chartrand, Chvátal, Cáceres, Cáceres, Delia Garijo, Fehr, Feng, Harary, Hughes, José Cáceres, Karen Meagher, Kaski, Kharaghani, Khuller, Kirkman, Lander, María Luz Puertas, Melter, Payne, Poisson, Robert F. Bailey, Sebő, Shanmukha, Slater, Valencia-Pabon   +37 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, Shahid ur Rehman, Muhammad Imran   +2 more
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Error-correcting codes from k-resolving sets

Discussiones Mathematicae Graph Theory, 2019
13 pages, 2 ...
Bailey, Robert F., González Yero, Ismael   +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, Nabilah Ayu Az-Zahra, Dafik, Antonius Cahya Prihandoko, Robiatul Adawiyah   +4 more
doaj   +1 more source

Resolvent Estimates for Normally Hyperbolic Trapped Sets [PDF]

Annales Henri Poincaré, 2011
Further changes to erratum correcting small problems with Section 3.5 and Lemma 4.1; this now also corrects hypotheses, explicitly requiring trapped set to be symplectic.
Wunsch, Jared, Zworski, Maciej
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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, Suma, A. S., Chandrakala, S. B.   +2 more
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