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    Wyświetlanie 1-8 z 8
    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:
    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:
    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:
    Maximal buttonings of trees
    Autorzy:
    Short, Ian
    Powiązania:
    https://bibliotekanauki.pl/articles/31232001.pdf
    Data publikacji:
    2014-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    centroid
    graph metric
    tree
    walk
    Wiener distance
    Opis:
    A buttoning of a tree that has vertices $v_1, v_2, . . ., v_n$ is a closed walk that starts at $v_1$ and travels along the shortest path in the tree to $v_2$, and then along the shortest path to $v_3$, and so forth, finishing with the shortest path from $v_n$ to $v_1$. Inspired by a problem about buttoning a shirt inefficiently, we determine the maximum length of buttonings of trees.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2014, 34, 2; 415-420
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The strong isometric dimension of finite reflexive graphs
    Autorzy:
    Fitzpatrick, Shannon
    Nowakowski, Richard
    Powiązania:
    https://bibliotekanauki.pl/articles/743675.pdf
    Data publikacji:
    2000
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    isometric
    embedding
    strong product
    injective hull
    paths
    distance
    metric
    Opis:
    The strong isometric dimension of a reflexive graph is related to its injective hull: both deal with embedding reflexive graphs in the strong product of paths. We give several upper and lower bounds for the strong isometric dimension of general graphs; the exact strong isometric dimension for cycles and hypercubes; and the isometric dimension for trees is found to within a factor of two.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2000, 20, 1; 23-38
    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:
    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
      Wyświetlanie 1-8 z 8

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