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    Wyświetlanie 1-7 z 7
    Tytuł:
    Radio numbers for generalized prism graphs
    Autorzy:
    Martinez, Paul
    Ortiz, Juan
    Tomova, Maggy
    Wyels, Cindy
    Powiązania:
    https://bibliotekanauki.pl/articles/744118.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    radio number
    radio labeling
    prism graphs
    Opis:
    A radio labeling is an assignment c:V(G) → N such that every distinct pair of vertices u,v satisfies the inequality d(u,v) + |c(u)-c(v)| ≥ diam(G) + 1. The span of a radio labeling is the maximum value. The radio number of G, rn(G), is the minimum span over all radio labelings of G. Generalized prism graphs, denoted $Z_{n,s}$, s ≥ 1, n ≥ s, have vertex set {(i,j) | i = 1,2 and j = 1,...,n} and edge set {((i,j),(i,j ±1))} ∪ {((1,i),(2,i+σ)) | σ = -⌊(s-1)/2⌋...,0,...,⌊s/2⌋}. In this paper we determine the radio number of $Z_{n,s}$ for s = 1,2 and 3. In the process we develop techniques that are likely to be of use in determining radio numbers of other families of graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2011, 31, 1; 45-62
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Radio Number of Cycles and their Total Graphs
    Autorzy:
    Merlin, E. T.
    Mangam, Tabitha Agnes
    Powiązania:
    https://bibliotekanauki.pl/articles/1177700.pdf
    Data publikacji:
    2018
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    Radio labeling
    Radio number
    Total graph
    Opis:
    A radio labeling f of G is an assignment of positive integers to the vertices of G satisfying, │f (u) – f (v)│≥ diam(G) + 1 - d (u ,v) ∀ u, v ∈ V (G) where d (u ,v) is the distance between any two vertices in the graph. The radio number denoted by rn (G) is the minimum span of a radio labeling for G. In this paper, an alternate proof for radio number of cycles and exact radio number for their total graphs has been discussed.
    Źródło:
    World Scientific News; 2018, 101; 55-64
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Radio number for some thorn graphs
    Autorzy:
    Marinescu-Ghemeci, Ruxandra
    Powiązania:
    https://bibliotekanauki.pl/articles/744574.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    multilevel distance labeling
    radio number
    caterpillar
    diameter
    Opis:
    For a graph G and any two vertices u and v in G, let d(u,v) denote the distance between u and v and let diam(G) be the diameter of G. A multilevel distance labeling (or radio labeling) for G is a function f that assigns to each vertex of G a positive integer such that for any two distinct vertices u and v, d(u,v) + |f(u) - f(v)| ≥ diam(G) + 1. The largest integer in the range of f is called the span of f and is denoted span(f). The radio number of G, denoted rn(G), is the minimum span of any radio labeling for G. A thorn graph is a graph obtained from a given graph by attaching new terminal vertices to the vertices of the initial graph. In this paper the radio numbers for two classes of thorn graphs are determined: the caterpillar obtained from the path Pₙ by attaching a new terminal vertex to each non-terminal vertex and the thorn star $S_{n,k}$ obtained from the star Sₙ by attaching k new terminal vertices to each terminal vertex of the star.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2010, 30, 2; 201-222
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Radio k-labelings for Cartesian products of graphs
    Autorzy:
    Kchikech, Mustapha
    Khennoufa, Riadh
    Togni, Olivier
    Powiązania:
    https://bibliotekanauki.pl/articles/743543.pdf
    Data publikacji:
    2008
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph theory
    radio channel assignment
    radio k-labeling
    Cartesian product
    radio number
    antipodal number
    Opis:
    Frequency planning consists in allocating frequencies to the transmitters of a cellular network so as to ensure that no pair of transmitters interfere. We study the problem of reducing interference by modeling this by a radio k-labeling problem on graphs: For a graph G and an integer k ≥ 1, a radio k-labeling of G is an assignment f of non negative integers to the vertices of G such that
    $|f(x)-f(y)| ≥ k+1-d_G(x,y)$,
    for any two vertices x and y, where $d_G(x,y)$ is the distance between x and y in G. The radio k-chromatic number is the minimum of max{f(x)-f(y):x,y ∈ V(G)} over all radio k-labelings f of G. In this paper we present the radio k-labeling for the Cartesian product of two graphs, providing upper bounds on the radio k-chromatic number for this product. These results help to determine upper and lower bounds for radio k-chromatic numbers of hypercubes and grids. In particular, we show that the ratio of upper and lower bounds of the radio number and the radio antipodal number of the square grid is asymptotically [3/2].
    Źródło:
    Discussiones Mathematicae Graph Theory; 2008, 28, 1; 165-178
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Radio Graceful Hamming Graphs
    Autorzy:
    Niedzialomski, Amanda
    Powiązania:
    https://bibliotekanauki.pl/articles/31340550.pdf
    Data publikacji:
    2016-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    radio labeling
    radio graceful graph
    Hamming graph
    Opis:
    For $ k \in \mathbb{Z}_+ $ and $G$ a simple, connected graph, a $k$-radio labeling $ f : V (G) \rightarrow \mathbb{Z}_+ $ of $G$ requires all pairs of distinct vertices $u$ and $v$ to satisfy $ |f(u) − f(v)| \ge k + 1 − d(u, v) $. We consider $k$-radio labelings of $G$ when $ k = \text{diam} (G)$. In this setting, $f$ is injective; if $f$ is also surjective onto $ {1, 2, . . ., |V (G)|} $, then $f$ is a consecutive radio labeling. Graphs that can be labeled with such a labeling are called radio graceful. In this paper, we give two results on the existence of radio graceful Hamming graphs. The main result shows that the Cartesian product of $t$ copies of a complete graph is radio graceful for certain $t$. Graphs of this form provide infinitely many examples of radio graceful graphs of arbitrary diameter. We also show that these graphs are not radio graceful for large $t$.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2016, 36, 4; 1007-1020
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On Radio Connection Number of Graphs
    Autorzy:
    Marinescu-Ghemeci, Ruxandra
    Powiązania:
    https://bibliotekanauki.pl/articles/31343294.pdf
    Data publikacji:
    2019-08-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    radio connection number
    radio coloring
    L (2, 1)-connection number
    L (2, 1)-connectivity
    L (2, 1)-labeling
    Opis:
    Given a graph G and a vertex coloring c, G is called l-radio connected if between any two distinct vertices u and v there is a path such that coloring c restricted to that path is an l-radio coloring. The smallest number of colors needed to make G l-radio connected is called the l-radio connection number of G. In this paper we introduce these notions and initiate the study of connectivity through radio colored paths, providing results on the 2-radio connection number, also called L(2, 1)-connection number: lower and upper bounds, existence problems, exact values for known classes of graphs and graph operations.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2019, 39, 3; 705-730
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Linear and cyclic radio k-labelings of trees
    Autorzy:
    Kchikech, Mustapha
    Khennoufa, Riadh
    Togni, Olivier
    Powiązania:
    https://bibliotekanauki.pl/articles/743693.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph theory
    radio channel assignment
    cyclic and linear radio k-labeling
    Opis:
    Motivated by problems in radio channel assignments, we consider radio k-labelings of graphs. For a connected graph G and an integer k ≥ 1, a linear radio k-labeling of G is an assignment f of nonnegative integers to the vertices of G such that
    $|f(x)-f(y)| ≥ k+1-d_G(x,y)$,
    for any two distinct vertices x and y, where $d_G(x,y)$ is the distance between x and y in G. A cyclic k-labeling of G is defined analogously by using the cyclic metric on the labels. In both cases, we are interested in minimizing the span of the labeling. The linear (cyclic, respectively) radio k-labeling number of G is the minimum span of a linear (cyclic, respectively) radio k-labeling of G. In this paper, linear and cyclic radio k-labeling numbers of paths, stars and trees are studied. For the path Pₙ of order n ≤ k+1, we completely determine the cyclic and linear radio k-labeling numbers. For 1 ≤ k ≤ n-2, a new improved lower bound for the linear radio k-labeling number is presented. Moreover, we give the exact value of the linear radio k-labeling number of stars and we present an upper bound for the linear radio k-labeling number of trees.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2007, 27, 1; 105-123
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-7 z 7

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