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    Tytuł:
    Minimal regular graphs with given girths and crossing numbers
    Autorzy:
    Chia, G.
    Gan, C.
    Powiązania:
    https://bibliotekanauki.pl/articles/744483.pdf
    Data publikacji:
    2004
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    regular graphs
    girth
    crossing numbers
    Opis:
    This paper investigates on those smallest regular graphs with given girths and having small crossing numbers.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2004, 24, 2; 223-237
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Interval edge colorings of some products of graphs
    Autorzy:
    Petrosyan, Petros
    Powiązania:
    https://bibliotekanauki.pl/articles/743918.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    edge coloring
    interval coloring
    regular graph
    products of graphs
    Opis:
    An edge coloring of a graph G with colors 1,2,...,t is called an interval t-coloring if for each i ∈ {1,2,...,t} there is at least one edge of G colored by i, and the colors of edges incident to any vertex of G are distinct and form an interval of integers. A graph G is interval colorable, if there is an integer t ≥ 1 for which G has an interval t-coloring. Let ℜ be the set of all interval colorable graphs. In 2004 Kubale and Giaro showed that if G,H ∈ , then the Cartesian product of these graphs belongs to . Also, they formulated a similar problem for the lexicographic product as an open problem. In this paper we first show that if G ∈ , then G[nK₁] ∈ for any n ∈ ℕ. Furthermore, we show that if G,H ∈ and H is a regular graph, then strong and lexicographic products of graphs G,H belong to . We also prove that tensor and strong tensor products of graphs G,H belong to if G ∈ and H is a regular graph.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2011, 31, 2; 357-373
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On composition of signed graphs
    Autorzy:
    Shahul Hameed, K.
    Germina, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/743222.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    signed graph
    eigenvalues
    graph composition
    regular graphs
    net-regular signed graphs
    Opis:
    A graph whose edges are labeled either as positive or negative is called a signed graph. In this article, we extend the notion of composition of (unsigned) graphs (also called lexicographic product) to signed graphs. We employ Kronecker product of matrices to express the adjacency matrix of this product of two signed graphs and hence find its eigenvalues when the second graph under composition is net-regular. A signed graph is said to be net-regular if every vertex has constant net-degree, namely, the difference of the number of positive and negative edges incident with a vertex. We also characterize balance in signed graph composition and have some results on the Laplacian matrices of this product.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2012, 32, 3; 507-516
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Signed star (k, k)-domatic number of a graph
    Autorzy:
    Sheikholeslami, S. M.
    Volkmann, L.
    Powiązania:
    https://bibliotekanauki.pl/articles/254927.pdf
    Data publikacji:
    2014
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    signed star (k, k)-domatic number
    signed star domatic number
    signed star k-dominating function
    signed star dominating function
    signed star k-domination number
    signed star domination number
    regular graphs
    Opis:
    Let G be a simple graph without isolated vertices with vertex set V (G) and edge set E(G) and let k be a positive integer. A function ƒ: E(G) →{−1, 1} is said to be a signed star k-dominating function on [formula] for every vertex v of G, where E(v) = {uv ∈ E(G) | u ∈ N(v)}. A set {f1, f2, . . . , fd} of signed star k-dominating functions on G with the property that [formula] for each e ∈ E(G) is called a signed star (k, k)-dominating family (of functions) on G. The maximum number of functions in a signed star (k, k)-dominating family on G is the signed star (k, k)-domatic number of G, denoted by [formula]. In this paper we study properties of the signed star (k, k)-domatic number [formula]. In particular, we present bounds on [formula], and we determine the signed (k, k)-domatic number of some regular graphs. Some of our results extend these given by Atapour, Sheikholeslami, Ghameslou and Volkmann [Signed star domatic number of a graph, Discrete Appl. Math. 158 (2010), 213–218] for the signed star domatic number.
    Źródło:
    Opuscula Mathematica; 2014, 34, 3; 609-620
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Upper Bounds on the Signed Total (k, k)-Domatic Number of Graphs
    Autorzy:
    Volkmann, Lutz
    Powiązania:
    https://bibliotekanauki.pl/articles/31339301.pdf
    Data publikacji:
    2015-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    signed total (k
    k)-domatic number
    signed total k-dominating function
    signed total k-domination number
    regular graphs
    Opis:
    Let $G$ be a graph with vertex set $V (G)$, and let $ f : V (G) \rightarrow {−1, 1}$ be a two-valued function. If $ k \geq 1$ is an integer and \( \sum_{ x \in N(v)} f(x) \geq k \) for each $ v \in V (G) $, where $N(v)$ is the neighborhood of $v$, then $f$ is a signed total $k$-dominating function on $G$. A set ${f_1, f_2, . . ., f_d}$ of distinct signed total k-dominating functions on $G$ with the property that \( \sum_{i=1}^d f_i(x) \leq k \) for each $ x \in V (G)$, is called a signed total ($k$, $k$)-dominating family (of functions) on $G$. The maximum number of functions in a signed total ($k$, $k$)-dominating family on $G$ is the signed total ($k$, $k$)-domatic number of $G$. In this article we mainly present upper bounds on the signed total ($k$, $k$)- domatic number, in particular for regular graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2015, 35, 4; 641-650
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A Note on the Locating-Total Domination in Graphs
    Autorzy:
    Miller, Mirka
    Rajan, R. Sundara
    Jayagopal, R.
    Rajasingh, Indra
    Manuel, Paul
    Powiązania:
    https://bibliotekanauki.pl/articles/31341658.pdf
    Data publikacji:
    2017-08-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    dominating set
    total dominating set
    locating-dominating set
    locating-total dominating set
    regular graphs
    Opis:
    In this paper we obtain a sharp (improved) lower bound on the locating-total domination number of a graph, and show that the decision problem for the locating-total domination is NP-complete.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2017, 37, 3; 745-754
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On edge product cordial graphs
    Autorzy:
    Ivanco, Jaroslav
    Powiązania:
    https://bibliotekanauki.pl/articles/255152.pdf
    Data publikacji:
    2019
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    edge product cordial labelings
    dense graphs
    regular graphs
    Opis:
    An edge product cordial labeling is a variant of the well-known cordial labeling. In this paper we characterize graphs admitting an edge product cordial labeling. Using this characterization we investigate the edge product cordiality of broad classes of graphs, namely, dense graphs, dense bipartite graphs, connected regular graphs, unions of some graphs, direct products of some bipartite graphs, joins of some graphs, maximal k-degenerate and related graphs, product cordial graphs.
    Źródło:
    Opuscula Mathematica; 2019, 39, 5; 691-703
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Regular Colorings in Regular Graphs
    Autorzy:
    Bernshteyn, Anton
    Khormali, Omid
    Martin, Ryan R.
    Rollin, Jonathan
    Rorabaugh, Danny
    Shan, Songling
    Uzzell, Andrew J.
    Powiązania:
    https://bibliotekanauki.pl/articles/31516306.pdf
    Data publikacji:
    2020-08-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    edge coloring
    graph factors
    regular graphs
    Opis:
    An (r − 1, 1)-coloring of an r-regular graph G is an edge coloring (with arbitrarily many colors) such that each vertex is incident to r − 1 edges of one color and 1 edge of a different color. In this paper, we completely characterize all 4-regular pseudographs (graphs that may contain parallel edges and loops) which do not have a (3, 1)-coloring. Also, for each r ≥ 6 we construct graphs that are not (r −1, 1)-colorable and, more generally, are not (r − t, t)-colorable for small t.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2020, 40, 3; 795-806
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Supermagic Graphs with Many Different Degrees
    Autorzy:
    Kovář, Petr
    Kravčenko, Michal
    Silber, Adam
    Krbeček, Matěj
    Powiązania:
    https://bibliotekanauki.pl/articles/32324150.pdf
    Data publikacji:
    2021-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph labeling
    supermagic labeling
    non-regular graphs
    Opis:
    Let G = (V, E) be a graph with n vertices and e edges. A supermagic labeling of G is a bijection f from the set of edges E to a set of consecutive integers {a, a + 1, . . ., a + e − 1} such that for every vertex v ∈ V the sum of labels of all adjacent edges equals the same constant k. This k is called a magic constant of f, and G is a supermagic graph. The existence of supermagic labeling for certain classes of graphs has been the scope of many papers. For a comprehensive overview see Gallian’s Dynamic survey of graph labeling in the Electronic Journal of Combinatorics. So far, regular or almost regular graphs have been studied. This is natural, since the same magic constant has to be achieved both at vertices of high degree as well as at vertices of low degree, while the labels are distinct consecutive integers.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2021, 41, 4; 1041-1050
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    b-Coloring of the Mycielskian of Some Classes of Graphs
    Autorzy:
    Raj, S. Francis
    Gokulnath, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/32361730.pdf
    Data publikacji:
    2022-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    b-coloring
    b-chromatic number
    Mycielskian of graphs
    regular graphs
    Opis:
    The b-chromatic number b(G) of a graph G is the maximum k for which G has a proper vertex coloring using k colors such that each color class contains at least one vertex adjacent to a vertex of every other color class. In this paper, we have mainly investigated on the b-chromatic number of the Mycielskian of regular graphs. In particular, we have obtained the exact value of the b-chromatic number of the Mycielskian of some classes of graphs. This includes a few families of regular graphs, graphs with b(G) = 2 and split graphs. In addition, we have found bounds for the b-chromatic number of the Mycielskian of some more families of regular graphs in terms of the bchromatic number of their original graphs. Also we have found b-chromatic number of the generalized Mycielskian of some regular graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2022, 42, 2; 363-381
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
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