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Wyszukujesz frazę "metric dimension" wg kryterium: Temat

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    Wyświetlanie 1-12 z 12
    Tytuł:
    Isometric embedding into spaces of continuous functions
    Autorzy:
    Villa, Rafael
    Powiązania:
    https://bibliotekanauki.pl/articles/1218403.pdf
    Data publikacji:
    1998
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    metric space
    Banach space
    metric linear dimension
    Opis:
    We prove that some Banach spaces X have the property that every Banach space that can be isometrically embedded in X can be isometrically and linearly embedded in X. We do not know if this is a general property of Banach spaces. As a consequence we characterize for which ordinal numbers α, β there exists an isometric embedding between $C_0(α+1)$ and $C_0(β+1)$.
    Źródło:
    Studia Mathematica; 1998, 129, 3; 197-205
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the Metric Dimension of Directed and Undirected Circulant Graphs
    Autorzy:
    Vetrík, Tomáš
    Powiązania:
    https://bibliotekanauki.pl/articles/31870010.pdf
    Data publikacji:
    2020-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    metric dimension
    resolving set
    circulant graph
    distance
    Opis:
    The undirected circulant graph $C_n(±1, ±2, . . ., ±t)$ consists of vertices $v_0, v_1, . . ., v_{n−1}$ and undirected edges $v_iv_{i+j}$, where $0 ≤ i ≤ n − 1, 1 ≤ j ≤ t (2 ≤ t ≤ \frac{n}{2})$, and the directed circulant graph $C_n(1, t)$ consists of vertices $v_0, v_1, . . ., v_{n−1}$ and directed edges $v_iv_{i+1}, v_iv_{i+t}$, where $0 ≤ i ≤ n − 1 (2 ≤ t ≤ n−1)$, the indices are taken modulo $n$. Results on the metric dimension of undirected circulant graphs $C_n(±1, ±t)$ are available only for special values of $t$. We give a complete solution of this problem for directed graphs $C_n(1, t)$ for every $t ≥ 2$ if $n ≥ 2t^2$. Grigorious et al. [On the metric dimension of circulant and Harary graphs, Appl. Math. Comput. 248 (2014) 47–54] presented a conjecture saying that dim $(C_n(±1, ±2, . . ., ±t)) = t + p − 1$ for $n = 2tk + t + p$, where $3 ≤ p ≤ t + 1$. We disprove it by showing that dim $(C_n(±1, ±2, . . ., ±t)) ≤ t + \frac{p+1}{2}$ for $n = 2tk + t + p$, where $t ≥ 4$ is even, $p$ is odd, $1 ≤ p ≤ t + 1$ and $k ≥ 1$.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2020, 40, 1; 67-76
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    All metric bases and fault-tolerant metric dimension for square of grid
    Autorzy:
    Saha, Laxman
    Basak, Mithun
    Tiwary, Kalishankar
    Powiązania:
    https://bibliotekanauki.pl/articles/2048644.pdf
    Data publikacji:
    2022
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    code
    resolving set
    metric dimension
    fault-tolerant resolving set
    fault-tolerant metric dimension
    Opis:
    For a simple connected graph G = (V,E) and an ordered subset W = {w1, w2, . . . , wk} of V , the code of a vertex v ∈ V , denoted by code(v), with respect to W is a k-tuple (d(v, w1), . . . , d(v, wk)), where d(v, wt) represents the distance between v and wt. The set W is called a resolving set of G if code(u) ≠ code(v) for every pair of distinct vertices u and v. A metric basis of G is a resolving set with the minimum cardinality. The metric dimension of G is the cardinality of a metric basis and is denoted by β(G). A set F ⊂ V is called fault-tolerant resolving set of G if F \ {v} is a resolving set of G for every v ∈ F. The fault-tolerant metric dimension of G is the cardinality of a minimal fault-tolerant resolving set. In this article, a complete characterization of metric bases for G2 mn has been given. In addition, we prove that the fault-tolerant metric dimension of G2 mn is 4 if m + n is even. We also show that the fault-tolerant metric dimension of G2 mn is at least 5 and at most 6 when m + n is odd.
    Źródło:
    Opuscula Mathematica; 2022, 42, 1; 93-111
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Metric dimension of Andrasfai graphs
    Autorzy:
    Pejman, S. Batool
    Payrovi, Shiroyeh
    Behtoei, Ali
    Powiązania:
    https://bibliotekanauki.pl/articles/254963.pdf
    Data publikacji:
    2019
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    resolving set
    metric dimension
    Andrasfai graph
    Cayley graph
    Cartesian product
    Opis:
    A set W ⊆ V(G) is called a resolving set, if for each pair of distinct vertices u,v ∈ V(G) there exists t ∈ W such that d(u,t) ≠ d(v,t), where d(x,y) is the distance between vertices x and y. The cardinality of a minimum resolving set for G is called the metric dimension of G and is denoted by dimM(G). This parameter has many applications in different areas. The problem of finding metric dimension is NP-complete for general graphs but it is determined for trees and some other important families of graphs. In this paper, we determine the exact value of the metric dimension of Andrasfai graphs, their complements and [formula]. Also, we provide upper and lower bounds for [formula].
    Źródło:
    Opuscula Mathematica; 2019, 39, 3; 415-423
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Closed Formulae for the Strong Metric Dimension of Lexicographic Product Graphs
    Autorzy:
    Kuziak, Dorota
    Yero, Ismael G.
    Rodríguez-Velázquez, Juan A.
    Powiązania:
    https://bibliotekanauki.pl/articles/31340465.pdf
    Data publikacji:
    2016-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    strong metric dimension
    strong metric basis
    strong metric generator
    lexicographic product graphs
    Opis:
    Given a connected graph G, a vertex w ∈ V (G) strongly resolves two vertices u, v ∈ V (G) if there exists some shortest u − w path containing v or some shortest v − w path containing u. A set S of vertices is a strong metric generator for G if every pair of vertices of G is strongly resolved by some vertex of S. The smallest cardinality of a strong metric generator for G is called the strong metric dimension of G. In this paper we obtain several relationships between the strong metric dimension of the lexicographic product of graphs and the strong metric dimension of its factor graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2016, 36, 4; 1051-1064
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Computing the Metric Dimension of a Graph from Primary Subgraphs
    Autorzy:
    Kuziak, Dorota
    Rodríguez-Velázquez, Juan A.
    Yero, Ismael G.
    Powiązania:
    https://bibliotekanauki.pl/articles/31342126.pdf
    Data publikacji:
    2017-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    metric dimension
    metric basis
    primary subgraphs
    rooted product graphs
    corona product graphs
    Opis:
    Let G be a connected graph. Given an ordered set W = {w1, . . ., wk} ⊆ V (G) and a vertex u ∈ V (G), the representation of u with respect to W is the ordered k-tuple (d(u, w1), d(u, w2), . . ., d(u, wk)), where d(u, wi) denotes the distance between u and wi. The set W is a metric generator for G if every two different vertices of G have distinct representations. A minimum cardinality metric generator is called a metric basis of G and its cardinality is called the metric dimension of G. It is well known that the problem of finding the metric dimension of a graph is NP-hard. In this paper we obtain closed formulae for the metric dimension of graphs with cut vertices. The main results are applied to specific constructions including rooted product graphs, corona product graphs, block graphs and chains of graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2017, 37, 1; 273-293
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The Hanoi Graph $H_4^3$
    Autorzy:
    Hinz, Andreas M.
    Movarraei, Nazanin
    Powiązania:
    https://bibliotekanauki.pl/articles/31348122.pdf
    Data publikacji:
    2020-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Hanoi graphs
    Sierpiński graphs
    metric dimension
    domination number
    dominator chromatic number
    Opis:
    Metric properties of Hanoi graphs $H_p^n$ are not as well understood as those of the closely related, but structurally simpler Sierpiński graphs $S_p^p$. The most outstanding open problem is to find the domination number of Hanoi graphs. Here we concentrate on the first non-trivial case of $H_4^3$, which contains no 1-perfect code. The metric dimension and the dominator chromatic number of $H_4^3$ will be determined as well. This leads to various conjectures for the general case and will thus provide an orientation for future research.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2020, 40, 4; 1095-1109
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The metric dimension of circulant graphs and their Cartesian products
    Autorzy:
    Chau, K.
    Gosselin, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/255804.pdf
    Data publikacji:
    2017
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    metric dimension
    circulant graph
    Cartesian product
    Opis:
    Let G = (V, E) be a connected graph (or hypergraph) and let d(x,y) denote the distance between vertices x,y ∈V(G). A subset W ⊆V(G) is called a resolving set for G if for every pair ol distinct vertices x, y ∈ (G), there is w ∈W such that d(x,w) ≠d(y,w). The minimum cardinality of a resolving set for G is called the metric dimension of G, denoted by β (G). The circulant graph Cn(l, 2,... , t) has vertex set {v0, v1 …, vn-1} and edges [formula] where 0 ≤ i ≤ n — 1 and 1 ≤j ≤ t and the indices are taken modulo [formula]. In this paper we determine the exact metric dimension olthe circulant graphs Cn(l, 2,... , t). extending previous results due to Borchert and Gosselin (2013), Grigorious et al. (2014), and Vetrik (2016). In particular, we show that [formula] for large enough n, which implies that the metric dimension ol these circulants is completely determined by the congruence class ol n modulo 2t. We determine the exact value of β Cn (l, 2,.. . , i)) for n ≡ 2 mod 2t and n =≡ (t + 1) mod 2t and we give better bounds on the metric dimension ol these circulants for n ≡ 0 mod 2t and n ≡ 1 mod 2t. In addition, we bound the metric dimension ol Cartesian products ol circulant graphs.
    Źródło:
    Opuscula Mathematica; 2017, 37, 4; 509-534
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Weak Total Resolvability In Graphs
    Autorzy:
    Casel, Katrin
    Estrada-Moreno, Alejandro
    Fernau, Henning
    Rodríguez-Velázquez, Juan Alberto
    Powiązania:
    https://bibliotekanauki.pl/articles/31341108.pdf
    Data publikacji:
    2016-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    metric dimension
    resolving set
    weak total metric dimension
    weak total resolving set
    adjacency dimension
    graph operations
    Opis:
    A vertex v ∈ V (G) is said to distinguish two vertices x, y ∈ V (G) of a graph G if the distance from v to x is di erent from the distance from v to y. A set W ⊆ V (G) is a total resolving set for a graph G if for every pair of vertices x, y ∈ V (G), there exists some vertex w ∈ W − {x, y} which distinguishes x and y, while W is a weak total resolving set if for every x ∈ V (G)−W and y ∈ W, there exists some w ∈ W −{y} which distinguishes x and y. A weak total resolving set of minimum cardinality is called a weak total metric basis of G and its cardinality the weak total metric dimension of G. Our main contributions are the following ones: (a) Graphs with small and large weak total metric bases are characterised. (b) We explore the (tight) relation to independent 2-domination. (c) We introduce a new graph parameter, called weak total adjacency dimension and present results that are analogous to those presented for weak total dimension. (d) For trees, we derive a characterisation of the weak total (adjacency) metric dimension. Also, exact figures for our parameters are presented for (generalised) fans and wheels. (e) We show that for Cartesian product graphs, the weak total (adjacency) metric dimension is usually pretty small. (f) The weak total (adjacency) dimension is studied for lexicographic products of graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2016, 36, 1; 185-210
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Error-Correcting Codes from k -Resolving Sets
    Autorzy:
    Bailey, Robert F.
    Yero, Ismael G.
    Powiązania:
    https://bibliotekanauki.pl/articles/31343451.pdf
    Data publikacji:
    2019-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    error-correcting code
    k -resolving set
    k -metric dimension
    covering design
    uncovering
    grid graph
    Opis:
    We demonstrate a construction of error-correcting codes from graphs by means of k-resolving sets, and present a decoding algorithm which makes use of covering designs. Along the way, we determine the k-metric dimension of grid graphs (i.e., Cartesian products of paths).
    Źródło:
    Discussiones Mathematicae Graph Theory; 2019, 39, 2; 341-355
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Stochastic diffrential equations on Banach spaces and their optimal feedback control
    Autorzy:
    Ahmed, N.U.
    Powiązania:
    https://bibliotekanauki.pl/articles/952179.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    stochastic differential equations
    Banach spaces
    optimal feedback control
    objective functionals
    Lévy-Prohorov metric
    Hausdorff dimension
    time-optimal problems
    Opis:
    In this paper we consider stochastic differential equations on Banach spaces (not Hilbert). The system is semilinear and the principal operator generating a C₀-semigroup is perturbed by a class of bounded linear operators considered as feedback operators from an admissible set. We consider the corresponding family of measure valued functions and present sufficient conditions for weak compactness. Then we consider applications of this result to several interesting optimal feedback control problems. We present results on existence of optimal feedback operators.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2012, 32, 1; 87-109
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-12 z 12

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