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    Wyświetlanie 1-13 z 13
    Tytuł:
    On the structure of compact graphs
    Autorzy:
    Nikandish, R.
    Shaveisi, F.
    Powiązania:
    https://bibliotekanauki.pl/articles/255638.pdf
    Data publikacji:
    2017
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    compact graph
    vertex degree
    cycle
    neighborhood
    Opis:
    A simple graph G is called a compact graph if G contains no isolated vertices and for each pair x, y of non-adjacent vertices of G, there is a vertex z with N(x) ∪ N(y) ⊆ N(z), where N(v) is the neighborhood of v, for every vertex v of G. In this paper, compact graphs with sufficient number of edges are studied. Also, it is proved that every regular compact graph is strongly regular. Some results about cycles in compact graphs are proved, too. Among other results, it is proved that if the ascending chain condition holds for the set of neighbors of a compact graph G, then the descending chain condition holds for the set of neighbors of G.
    Źródło:
    Opuscula Mathematica; 2017, 37, 6; 875-886
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the multiplicative Zagreb coindex of graphs
    Autorzy:
    Xu, K.
    Das, K. Ch.
    Tang, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/254706.pdf
    Data publikacji:
    2013
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    vertex degree
    tree
    upper or lower bound
    Opis:
    For a (molecular) graph G with vertex set V (G) and edge set E(G), the first and second Zagreb indices of G are defined as [formula] and [formula] respectively, where dG(v) is the degree of vertex v in G. The alternative expression of M1 (G) is [formula]. Recently Ashrafi, Doslic and Hamzeh introduced two related graphical invariants [formula] and [formula] named as first Zagreb coindex and second Zagreb coindex, respectively. Here we define two new graphical invariants [formula] and [formula] as the respective multiplicative versions of [formula]. In this paper, we have reported some properties, especially upper and lower bounds, for these two graph invariants of connected (molecular) graphs. Moreover, some corresponding extremal graphs have been characterized with respect to these two indices.
    Źródło:
    Opuscula Mathematica; 2013, 33, 1; 191-204
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Families of triples with high minimum degree are Hamiltonian
    Autorzy:
    Rödl, Vojtech
    Ruciński, Andrzej
    Powiązania:
    https://bibliotekanauki.pl/articles/30148238.pdf
    Data publikacji:
    2014-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    3-uniform hypergraph
    Hamilton cycle
    minimum vertex degree
    Opis:
    In this paper we show that every family of triples, that is, a 3-uniform hypergraph, with minimum degree at least $$(\frac{5−√5}{3} + γ)\binom{n−1}{2}$$ contains a tight Hamiltonian cycle.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2014, 34, 2; 361-381
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An application of graph theory to linguistic complexity
    Autorzy:
    Piperski, Alexander
    Powiązania:
    https://bibliotekanauki.pl/articles/1151871.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet im. Adama Mickiewicza w Poznaniu
    Tematy:
    linguistic complexity
    morphology
    graph theory
    average vertex degree
    Opis:
    This article introduces a new measure of linguistic complexity which is based on the dual nature of the linguistic sign. Complexity is analyzed as consisting of three components, namely the conceptual complexity (complexity of the signified), the formal complexity (complexity of the signifier) and the form-meaning correspondence complexity. I describe a way of plotting the form-meaning relationship on a graph with two tiers (the form tier and the meaning tier) and apply a complexity measure from graph theory (average vertex degree) to assess the complexity of such graphs. The proposed method is illustrated by estimating the complexity of full noun phrases (determiner + adjective + noun) in English, Swedish, and German. I also mention the limitations and the problems which might arise when using this method.
    Źródło:
    Yearbook of the Poznań Linguistic Meeting; 2014, 1, 1
    2449-7525
    Pojawia się w:
    Yearbook of the Poznań Linguistic Meeting
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An application of graph theory to linguistic complexity
    Autorzy:
    Piperski, Alexander
    Powiązania:
    https://bibliotekanauki.pl/articles/2135360.pdf
    Data publikacji:
    2014-11-19
    Wydawca:
    Uniwersytet im. Adama Mickiewicza w Poznaniu
    Tematy:
    linguistic complexity
    morphology
    graph theory
    average vertex degree
    Opis:
    This article introduces a new measure of linguistic complexity which is based on the dual nature of the linguistic sign. Complexity is analyzed as consisting of three components, namely the conceptual complexity (complexity of the signified), the formal complexity (complexity of the signifier) and the form-meaning correspondence complexity. I describe a way of plotting the form-meaning relationship on a graph with two tiers (the form tier and the meaning tier) and apply a complexity measure from graph theory (average vertex degree) to assess the complexity of such graphs. The proposed method is illustrated by estimating the complexity of full noun phrases (determiner + adjective + noun) in English, Swedish, and German. I also mention the limitations and the problems which might arise when using this method.
    Źródło:
    Yearbook of the Poznań Linguistic Meeting; 2014, 1, 1; 89-102
    2449-7525
    Pojawia się w:
    Yearbook of the Poznań Linguistic Meeting
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    5-stars of low weight in normal plane maps with minimum degree 5
    Autorzy:
    Borodin, Oleg V.
    Ivanova, Anna O.
    Jensen, Tommy R.
    Powiązania:
    https://bibliotekanauki.pl/articles/30148303.pdf
    Data publikacji:
    2014-08-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph
    plane map
    vertex degree
    weight
    light subgraph
    Opis:
    It is known that there are normal plane maps $M_5$ with minimum degree 5 such that the minimum degree-sum $w(S_5)$ of 5-stars at 5-vertices is arbitrarily large. In 1940, Lebesgue showed that if an $M_5$ has no 4-stars of cyclic type (5, 6, 6, 5) centered at 5-vertices, then $w(S_5) ≤ 68$. We improve this bound of 68 to 55 and give a construction of a (5, 6, 6, 5)-free $M_5$ with $w(S_5) = 48$.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2014, 34, 3; 539-546
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Open support of some special types of graphs under addition
    Autorzy:
    Jeyalakshmi, M.
    Meena, N.
    Powiązania:
    https://bibliotekanauki.pl/articles/1193410.pdf
    Data publikacji:
    2021
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    degree of a vertex
    open neighbourhood of a vertex
    open support of a graph
    open support of a vertex
    Opis:
    A open support of a vertex v under addition is defined by ∑_(u ∈N(v))▒deg〖(u)〗 and it is denoted by supp(v). A open support of a graph under addition is defined by ∑_(v ∈V(G))▒supp〖(v)〗 and it is denoted by supp(G). In this paper, open support of some graphs is studied.
    Źródło:
    World Scientific News; 2021, 156; 130-146
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Vertex-disjoint stars in graphs
    Autorzy:
    Ota, Katsuhiro
    Powiązania:
    https://bibliotekanauki.pl/articles/743470.pdf
    Data publikacji:
    2001
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    stars
    vertex-disjoint copies
    minimum degree
    Opis:
    In this paper, we give a sufficient condition for a graph to contain vertex-disjoint stars of a given size. It is proved that if the minimum degree of the graph is at least k+t-1 and the order is at least (t+1)k + O(t²), then the graph contains k vertex-disjoint copies of a star $K_{1,t}$. The condition on the minimum degree is sharp, and there is an example showing that the term O(t²) for the number of uncovered vertices is necessary in a sense.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2001, 21, 2; 179-185
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the Rainbow Vertex-Connection
    Autorzy:
    Li, Xueliang
    Shi, Yongtang
    Powiązania:
    https://bibliotekanauki.pl/articles/30146636.pdf
    Data publikacji:
    2013-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    rainbow vertex-connection
    vertex coloring
    minimum degree
    2-step dominating set
    Opis:
    A vertex-colored graph is rainbow vertex-connected if any two vertices are connected by a path whose internal vertices have distinct colors. The rainbow vertex-connection of a connected graph $G$, denoted by $rvc(G)$, is the smallest number of colors that are needed in order to make $G$ rainbow vertex-connected. It was proved that if $G$ is a graph of order $n$ with minimum degree $ \delta $, then $ rvc(G) < 11n//\delta$. In this paper, we show that $rvc(G) \le 3n//(δ+1)+5$ for $ \delta \ge \sqrt{n-1} -1 $ and $ n \le 290 $, while $ rvc(G) \le 4n//(δ + 1) + 5 $ for $ 16 \le \delta \le \sqrt{n-1}-2 $ and $ rvc(G) \le 4n//(\delta + 1) + C(\delta) $ for $6 \le \delta \le 15$, where $ C(\delta) = e^\frac{ 3 \log (\delta^3 + 2 \delta^2 +3)-3(\log 3 - 1)}{\delta - 3} - 2$. We also prove that $ rvc(G) \le 3n//4 − 2 $ for $ \delta = 3$, $ rvc(G) \le 3n//5 − 8//5$ for $\delta = 4$ and $rvc(G) \le n//2 − 2$ for $\delta = 5$. Moreover, an example constructed by Caro et al. shows that when $ \delta \ge \sqrt{n-1} - 1 $ and $ \delta = 3, 4, 5 $, our bounds are seen to be tight up to additive constants.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2013, 33, 2; 307-313
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Vertex-disjoint copies of K¯₄
    Autorzy:
    Kawarabayashi, Ken-ichi
    Powiązania:
    https://bibliotekanauki.pl/articles/744487.pdf
    Data publikacji:
    2004
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    extremal graph theory
    vertex disjoint copy
    minimum degree
    Opis:
    Let G be a graph of order n. Let K¯ₗ be the graph obtained from Kₗ by removing one edge.
    In this paper, we propose the following conjecture:
    Let G be a graph of order n ≥ lk with δ(G) ≥ (n-k+1)(l-3)/(l-2)+k-1. Then G has k vertex-disjoint K¯ₗ.
    This conjecture is motivated by Hajnal and Szemerédi's [6] famous theorem. In this paper, we verify this conjecture for l=4.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2004, 24, 2; 249-262
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Heavy cycles in weighted graphs
    Autorzy:
    Bondy, J.
    Broersma, Hajo
    van den Heuvel, Jan
    Veldman, Henk
    Powiązania:
    https://bibliotekanauki.pl/articles/743527.pdf
    Data publikacji:
    2002
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    weighted graph
    (long, optimal, Hamilton) cycle
    (edge-, vertex-)weighting
    weighted degree
    Opis:
    An (edge-)weighted graph is a graph in which each edge e is assigned a nonnegative real number w(e), called the weight of e. The weight of a cycle is the sum of the weights of its edges, and an optimal cycle is one of maximum weight. The weighted degree w(v) of a vertex v is the sum of the weights of the edges incident with v. The following weighted analogue (and generalization) of a well-known result by Dirac for unweighted graphs is due to Bondy and Fan. Let G be a 2-connected weighted graph such that w(v) ≥ r for every vertex v of G. Then either G contains a cycle of weight at least 2r or every optimal cycle of G is a Hamilton cycle. We prove the following weighted analogue of a generalization of Dirac's result that was first proved by Pósa. Let G be a 2-connected weighted graph such that w(u)+w(v) ≥ s for every pair of nonadjacent vertices u and v. Then G contains either a cycle of weight at least s or a Hamilton cycle. Examples show that the second conclusion cannot be replaced by the stronger second conclusion from the result of Bondy and Fan. However, we characterize a natural class of edge-weightings for which these two conclusions are equivalent, and show that such edge-weightings can be recognized in time linear in the number of edges.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2002, 22, 1; 7-15
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the hat problem on a graph
    Autorzy:
    Krzywkowski, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/256048.pdf
    Data publikacji:
    2012
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    hat problem
    graph
    degree
    neighborhood
    neighborhood-dominated
    unicyclic
    universal vertex
    Nordhaus-Gaddum
    Opis:
    The topic of this paper is the hat problem in which each of n players is uniformly and independently fitted with a blue or red hat. Then everybody can try to guess simultaneously his own hat color by looking at the hat colors of the other players. The team wins if at least one player guesses his hat color correctly, and no one guesses his hat color wrong; otherwise the team loses. The aim is to maximize the probability of winning. In this version every player can see everybody excluding himself. We consider such a problem on a graph, where vertices correspond to players, and a player can see each player to whom he is connected by an edge. The solution of the hat problem on a graph is known for trees and for cycles on four or at least nine vertices. In this paper first we give an upper bound on the maximum chance of success for graphs with neighborhood-dominated vertices. Next we solve the problem on unicyclic graphs containing a cycle on at least nine vertices. We prove that the maximum chance of success is one by two. Then we consider the hat problem on a graph with a universal vertex. We prove that there always exists an optimal strategy such that in every case some vertex guesses its color. Moreover, we prove that there exists a graph with a universal vertex for which there exists an optimal strategy such that in some case no vertex guesses its color. We also give some Nordhaus-Gaddum type inequalities.
    Źródło:
    Opuscula Mathematica; 2012, 32, 2; 285-296
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Spectral Radius and Hamiltonicity of Graphs
    Autorzy:
    Yu, Guidong
    Fang, Yi
    Fan, Yizheng
    Cai, Gaixiang
    Powiązania:
    https://bibliotekanauki.pl/articles/31343181.pdf
    Data publikacji:
    2019-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    spectral radius
    singless Laplacian spectral radius
    traceable
    Hamiltonian-connected
    traceable from every vertex
    minimum degree
    Opis:
    In this paper, we study the Hamiltonicity of graphs with large minimum degree. Firstly, we present some conditions for a simple graph to be Hamilton-connected and traceable from every vertex in terms of the spectral radius of the graph or its complement, respectively. Secondly, we give the conditions for a nearly balanced bipartite graph to be traceable in terms of spectral radius, signless Laplacian spectral radius of the graph or its quasi-complement, respectively.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2019, 39, 4; 951-974
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-13 z 13

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