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    Wyświetlanie 1-8 z 8
    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:
    Pair L(2, 1)-Labelings of Infinite Graphs
    Autorzy:
    Yeh, Roger K.
    Powiązania:
    https://bibliotekanauki.pl/articles/31343562.pdf
    Data publikacji:
    2019-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    L(2
    1)-labeling
    Opis:
    An L(2, 1)-labeling of a graph G = (V,E) is an assignment of nonnegative integers to V such that two adjacent vertices must receive numbers (labels) at least two apart and further, if two vertices are in distance 2 then they receive distinct labels. This article studies a generalization of the L(2, 1)-labeling. We assign sets with at least one element to vertices of G under some conditions.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2019, 39, 1; 257-269
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On L(2, 1)-Labelings of Oriented Graphs
    Autorzy:
    Colucci, Lucas
    Győri, Ervin
    Powiązania:
    https://bibliotekanauki.pl/articles/32361754.pdf
    Data publikacji:
    2022-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    L (2,1)-labeling
    directed graphs
    Opis:
    We extend a result of Griggs and Yeh about the maximum possible value of the L(2, 1)-labeling number of a graph in terms of its maximum degree to oriented graphs. We consider the problem both in the usual definition of the oriented L(2, 1)-labeling number and in some variants we introduce.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2022, 42, 1; 39-46
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Characterization Results for the L(2, 1, 1)-Labeling Problem on Trees
    Autorzy:
    Zhang, Xiaoling
    Deng, Kecai
    Powiązania:
    https://bibliotekanauki.pl/articles/32031843.pdf
    Data publikacji:
    2017-08-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    tree
    diameter
    L(2, 1, 1)-labeling
    Opis:
    An L(2, 1, 1)-labeling of a graph G is an assignment of non-negative integers (labels) to the vertices of G such that adjacent vertices receive labels with difference at least 2, and vertices at distance 2 or 3 receive distinct labels. The span of such a labelling is the difference between the maximum and minimum labels used, and the minimum span over all L(2, 1, 1)-labelings of G is called the L(2, 1, 1)-labeling number of G, denoted by λ2,1,1(G). It was shown by King, Ras and Zhou in [The L(h, 1, 1)-labelling problem for trees, European J. Combin. 31 (2010) 1295–1306] that every tree T has Δ2(T) − 1 ≤ λ2,1,1(T) ≤ Δ2(T), where Δ2(T) = maxuv∈E(T)(d(u) + d(v)). And they conjectured that almost all trees have the L(2, 1, 1)-labeling number attain the lower bound. This paper provides some sufficient conditions for λ2,1,1(T) = Δ2(T). Furthermore, we show that the sufficient conditions we provide are also necessary for trees with diameter at most 6.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2017, 37, 3; 611-622
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    L(2, 1)-Labeling of Circulant Graphs
    Autorzy:
    Mitra, Sarbari
    Bhoumik, Soumya
    Powiązania:
    https://bibliotekanauki.pl/articles/31343649.pdf
    Data publikacji:
    2019-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph coloring
    L(2
    1)-labeling
    circulants
    Opis:
    An $L(2, 1)$-labeling of a graph $ \Gamma $ is an assignment of non-negative integers to the vertices such that adjacent vertices receive labels that differ by at least 2, and those at a distance of two receive labels that differ by at least one. Let $ \lambda_2^1 (\Gamma) $ denote the least $ \lambda $ such that $ \Gamma $ admits an $ L(2, 1) $-labeling using labels from $ \{ 0, 1, . . ., \lambda \} $. A Cayley graph of group $G$ is called a circulant graph of order $n$, if $ G = \mathbb{Z}_n$. In this paper initially we investigate the upper bound for the span of the $L(2, 1)$-labeling for Cayley graphs on cyclic groups with “large” connection sets. Then we extend our observation and find the span of $L(2, 1)$-labeling for any circulants of order $n$.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2019, 39, 1; 143-155
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    L(2, 1)-Labelings of Some Families of Oriented Planar Graphs
    Autorzy:
    Sen, Sagnik
    Powiązania:
    https://bibliotekanauki.pl/articles/30147217.pdf
    Data publikacji:
    2014-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    homomorphism
    planar graph
    girth
    partial k-tree
    outerplanar graph
    cactus
    2-dipath L(2, 1)-labeling
    oriented L(2, 1)-labeling
    Opis:
    In this paper we determine, or give lower and upper bounds on, the 2-dipath and oriented L(2, 1)-span of the family of planar graphs, planar graphs with girth 5, 11, 16, partial k-trees, outerplanar graphs and cacti.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2014, 34, 1; 31-48
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Solutions of Some L(2, 1)-Coloring Related Open Problems
    Autorzy:
    Mandal, Nibedita
    Panigrahi, Pratima
    Powiązania:
    https://bibliotekanauki.pl/articles/31341092.pdf
    Data publikacji:
    2016-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    span of a graph
    no-hole coloring
    irreducible coloring
    unicyclic graph
    L(2 1)-coloring
    Opis:
    An L(2, 1)-coloring (or labeling) of a graph G is a vertex coloring f : V (G) → Z+ ∪ {0} such that |f(u) − f(v)| ≥ 2 for all edges uv of G, and |f(u)−f(v)| ≥ 1 if d(u, v) = 2, where d(u, v) is the distance between vertices u and v in G. The span of an L(2, 1)-coloring is the maximum color (or label) assigned by it. The span of a graph G is the smallest integer λ such that there exists an L(2, 1)-coloring of G with span λ. An L(2, 1)-coloring of a graph with span equal to the span of the graph is called a span coloring. For an L(2, 1)-coloring f of a graph G with span k, an integer h is a hole in f if h ∈ (0, k) and there is no vertex v in G such that f(v) = h. A no-hole coloring is an L(2, 1)-coloring with no hole in it. An L(2, 1)-coloring is irreducible if color of none of the vertices in the graph can be decreased to yield another L(2, 1)-coloring of the same graph. A graph G is inh-colorable if there exists an irreducible no-hole coloring of G. Most of the results obtained in this paper are answers to some problems asked by Laskar et al. [5]. These problems are mainly about relationship between the span and maximum no-hole span of a graph, lower inh-span and upper inh-span of a graph, and the maximum number of holes and minimum number of holes in a span coloring of a graph. We also give some sufficient conditions for a tree and an unicyclic graph to have inh-span Δ + 1.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2016, 36, 2; 279-297
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Irreducible No-Hole L(2, 1)-Coloring of Edge-Multiplicity-Paths-Replacement Graph
    Autorzy:
    Mandal, Nibedita
    Panigrahi, Pratima
    Powiązania:
    https://bibliotekanauki.pl/articles/31342318.pdf
    Data publikacji:
    2018-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    L (2,1)-coloring
    no-hole coloring
    irreducible coloring
    subdivision graph
    edge-multiplicity-paths-replacement graph
    Opis:
    An L(2, 1)-coloring (or labeling) of a simple connected graph G is a mapping f : V (G) → Z+ ∪ {0} such that |f(u)−f(v)| ≥ 2 for all edges uv of G, and |f(u) − f(v)| ≥ 1 if u and v are at distance two in G. The span of an L(2, 1)-coloring f, denoted by span(f), of G is max{f(v) : v ∈ V (G)}. The span of G, denoted by λ(G), is the minimum span of all possible L(2, 1)-colorings of G. For an L(2, 1)-coloring f of a graph G with span k, an integer l is a hole in f if l ∈ (0, k) and there is no vertex v in G such that f(v) = l. An L(2, 1)-coloring is a no-hole coloring if there is no hole in it, and is an irreducible coloring if color of none of the vertices in the graph can be decreased and yield another L(2, 1)-coloring of the same graph. An irreducible no-hole coloring, in short inh-coloring, of G is an L(2, 1)-coloring of G which is both irreducible and no-hole. For an inh-colorable graph G, the inh-span of G, denoted by λinh(G), is defined as λinh(G) = min{span(f) : f is an inh-coloring of G. Given a function h : E(G) → ℕ − {1}, and a positive integer r ≥ 2, the edge-multiplicity-paths-replacement graph G(rPh) of G is the graph obtained by replacing every edge uv of G with r paths of length h(uv) each. In this paper we show that G(rPh) is inh-colorable except possibly the cases h(e) ≥ 2 with equality for at least one but not for all edges e and (i) Δ(G) = 2, r = 2 or (ii) Δ (G) ≥ 3, 2 ≤ r ≤ 4. We find the exact value of λinh(G(rPh)) in several cases and give upper bounds of the same in the remaining. Moreover, we find the value of λ(G(rPh)) in most of the cases which were left by Lü and Sun in [L(2, 1)-labelings of the edge-multiplicity-paths-replacement of a graph, J. Comb. Optim. 31 (2016) 396–404].
    Źródło:
    Discussiones Mathematicae Graph Theory; 2018, 38, 2; 525-552
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-8 z 8

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