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Tytuł:
Iterated neighborhood graphs
Autorzy:
Sonntag, Martin
Teichert, Hanns-Martin
Powiązania:
https://bibliotekanauki.pl/articles/743216.pdf
Data publikacji:
2012
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
neighborhood graph
2-step graph
neighborhood completeness number
Opis:
The neighborhood graph N(G) of a simple undirected graph G = (V,E) is the graph $(V,E_N)$ where $E_N$ = {{a,b} | a ≠ b, {x,a} ∈ E and {x,b} ∈ E for some x ∈ V}. It is well-known that the neighborhood graph N(G) is connected if and only if the graph G is connected and non-bipartite.
We present some results concerning the k-iterated neighborhood graph $N^k(G) : = N(N(...N(G)))$ of G. In particular we investigate conditions for G and k such that $N^k(G)$ becomes a complete graph.
Źródło:
Discussiones Mathematicae Graph Theory; 2012, 32, 3; 403-417
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Graph Operations and Neighborhood Polynomials
Autorzy:
Alipour, Maryam
Tittmann, Peter
Powiązania:
https://bibliotekanauki.pl/articles/32083862.pdf
Data publikacji:
2021-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
neighborhood complex
neighborhood polynomial
domination polynomial
graph operations
graph degeneracy
Opis:
The neighborhood polynomial of graph G is the generating function for the number of vertex subsets of G of which the vertices have a common neighbor in G. In this paper, we investigate the behavior of this polynomial under several graph operations. Specifically, we provide an explicit formula for the neighborhood polynomial of the graph obtained from a given graph G by vertex attachment. We use this result to propose a recursive algorithm for the calculation of the neighborhood polynomial. Finally, we prove that the neighborhood polynomial can be found in polynomial-time in the class of k-degenerate graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2021, 41, 3; 697-711
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Long cycles and neighborhood union in 1-tough graphs with large degree sums
Autorzy:
Hoa, Vu
Powiązania:
https://bibliotekanauki.pl/articles/972054.pdf
Data publikacji:
1998
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graphs
neighborhood
toughness
cycles
Opis:
For a 1-tough graph G we define σ₃(G) = min{d(u) + d(v) + d(w):{u,v,w} is an independent set of vertices} and $NC_{σ₃-n+5}(G)$ = $max{⋃_{i = 1}^{σ₃-n+5}$ $N(v_i) : {v₁, ..., v_{σ₃-n+5}}$ is an independent set of vertices}. We show that every 1-tough graph with σ₃(G) ≥ n contains a cycle of length at least $min{n,2NC_{σ₃-n+5}(G)+2}$. This result implies some well-known results of Faßbender [2] and of Flandrin, Jung & Li [6]. The main result of this paper also implies that c(G) ≥ min{n,2NC₂(G)+2} where NC₂(G) = min{|N(u) ∪ N(v)|:d(u,v) = 2}. This strengthens a result that c(G) ≥ min{n, 2NC₂(G)} of Bauer, Fan and Veldman [3].
Źródło:
Discussiones Mathematicae Graph Theory; 1998, 18, 1; 5-13
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:
Distance-Locally Disconnected Graphs
Autorzy:
Miller, Mirka
Ryan, Joe
Ryjáček, Zdeněk
Powiązania:
https://bibliotekanauki.pl/articles/30146681.pdf
Data publikacji:
2013-03-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
neighborhood
distance
locally disconnected
cage
Opis:
For an integer k ≥ 1, we say that a (finite simple undirected) graph G is k-distance-locally disconnected, or simply k-locally disconnected if, for any x ∈ V (G), the set of vertices at distance at least 1 and at most k from x induces in G a disconnected graph. In this paper we study the asymptotic behavior of the number of edges of a k-locally disconnected graph on n vertices. For general graphs, we show that this number is Θ(n2) for any fixed value of k and, in the special case of regular graphs, we show that this asymptotic rate of growth cannot be achieved. For regular graphs, we give a general upper bound and we show its asymptotic sharpness for some values of k. We also discuss some connections with cages.
Źródło:
Discussiones Mathematicae Graph Theory; 2013, 33, 1; 203-215
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Almost Injective Colorings
Autorzy:
Goddard, Wayne
Melville, Robert
Xu, Honghai
Powiązania:
https://bibliotekanauki.pl/articles/31343577.pdf
Data publikacji:
2019-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
coloring
injective
closed neighborhood
domatic
Opis:
We define an almost-injective coloring as a coloring of the vertices of a graph such that every closed neighborhood has exactly one duplicate. That is, every vertex has either exactly one neighbor with the same color as it, or exactly two neighbors of the same color. We present results with regards to the existence of such a coloring and also the maximum (minimum) number of colors for various graph classes such as complete k-partite graphs, trees, and Cartesian product graphs. In particular, we give a characterization of trees that have an almost-injective coloring. For such trees, we show that the minimum number of colors equals the maximum degree, and we also provide a polynomial-time algorithm for computing the maximum number of colors, even though these questions are NP-hard for general graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2019, 39, 1; 225-239
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Graph Exponentiation and Neighborhood Reconstruction
Autorzy:
Hammack, Richard H.
Powiązania:
https://bibliotekanauki.pl/articles/32083841.pdf
Data publikacji:
2021-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
neighborhood reconstructible graphs
graph exponentiation
Opis:
Any graph $G$ admits a neighborhood multiset \(\mathscr{N}(G) = \{N_G(x) | x ∈ V (G)\}\) whose elements are precisely the open neighborhoods of $G$. We say $G$ is neighborhood reconstructible if it can be reconstructed from \(\mathscr{N}(G)\), that is, if \(G ≅ H\) whenever \(\mathscr{N}(G) = \mathscr{N}(H)\) for some other graph $H$. This note characterizes neighborhood reconstructible graphs as those graphs $G$ that obey the exponential cancellation \(G^{K_2} ≅ H^{K_2} ⇒ G ≅ H\).
Źródło:
Discussiones Mathematicae Graph Theory; 2021, 41, 1; 335-339
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
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:
Extension of several sufficient conditions for Hamiltonian graphs
Autorzy:
Ainouche, Ahmed
Powiązania:
https://bibliotekanauki.pl/articles/744192.pdf
Data publikacji:
2006
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hamiltonian graph
dual closure
neighborhood closure
Opis:
Let G be a 2-connected graph of order n. Suppose that for all 3-independent sets X in G, there exists a vertex u in X such that |N(X∖{u})|+d(u) ≥ n-1. Using the concept of dual closure, we prove that
1. G is hamiltonian if and only if its 0-dual closure is either complete or the cycle C₇
2. G is nonhamiltonian if and only if its 0-dual closure is either the graph $(K_r ∪ Kₛ ∪ Kₜ) ∨ K₂$, 1 ≤ r ≤ s ≤ t or the graph $((n+1)/2)K₁ ∨ K_{(n-1)/2}$.
It follows that it takes a polynomial time to check the hamiltonicity or the nonhamiltonicity of a graph satisfying the above condition. From this main result we derive a large number of extensions of previous sufficient conditions for hamiltonian graphs. All these results are sharp.
Źródło:
Discussiones Mathematicae Graph Theory; 2006, 26, 1; 23-39
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Designing WDM networks by a variable neighborhood search
Autorzy:
Melian-Batista, B.
Höller, H.
Voss, S.
Powiązania:
https://bibliotekanauki.pl/articles/308920.pdf
Data publikacji:
2006
Wydawca:
Instytut Łączności - Państwowy Instytut Badawczy
Tematy:
network design
WDM
SDH
variable neighborhood search
Opis:
With the ever-rising data volume that is demanded by the market, network planning in order to minimize the necessary investment while meeting the demands is constantly an important task for the network providers. Synchronous digital hierarchy (SDH) and wavelength division multiplex (WDM) form the core of many current backbone networks. In order to solve the provisioning and routing problem in such WDM networks, we develop a variable neighborhood search (VNS) metaheuristic. VNS is a metaheuristic that combines series of random and improving local searches based on systematically changed neighborhoods. An integer flow formulation is modeled in AMPL and solved by CPLEX in order to obtain optimal solutions as a reference for the heuristic.
Źródło:
Journal of Telecommunications and Information Technology; 2006, 4; 15-20
1509-4553
1899-8852
Pojawia się w:
Journal of Telecommunications and Information Technology
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Describing Neighborhoods of 5-Vertices in 3-Polytopes with Minimum Degree 5 and Without Vertices of Degrees from 7 to 11
Autorzy:
Borodin, Oleg V.
Ivanova, Anna O.
Kazak, Olesya N.
Powiązania:
https://bibliotekanauki.pl/articles/31342287.pdf
Data publikacji:
2018-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
planar graph
structure properties
3-polytope
neighborhood
Opis:
In 1940, Lebesgue proved that every 3-polytope contains a 5-vertex for which the set of degrees of its neighbors is majorized by one of the following sequences: (6, 6, 7, 7, 7), (6, 6, 6, 7, 9), (6, 6, 6, 6, 11), (5, 6, 7, 7, 8), (5, 6, 6, 7, 12), (5, 6, 6, 8, 10), (5, 6, 6, 6, 17), (5, 5, 7, 7, 13), (5, 5, 7, 8, 10), (5, 5, 6, 7, 27), (5, 5, 6, 6, ∞), (5, 5, 6, 8, 15), (5, 5, 6, 9, 11), (5, 5, 5, 7, 41), (5, 5, 5, 8, 23), (5, 5, 5, 9, 17), (5, 5, 5, 10, 14), (5, 5, 5, 11, 13). In this paper we prove that every 3-polytope without vertices of degree from 7 to 11 contains a 5-vertex for which the set of degrees of its neighbors is majorized by one of the following sequences: (5, 5, 6, 6, ∞), (5, 6, 6, 6, 15), (6, 6, 6, 6, 6), where all parameters are tight.
Źródło:
Discussiones Mathematicae Graph Theory; 2018, 38, 3; 615-625
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Intrinsic dimensionality detection criterion based on Locally Linear Embedding
Autorzy:
Meng, L.
Breitkopf, P.
Powiązania:
https://bibliotekanauki.pl/articles/952945.pdf
Data publikacji:
2018
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
LLE
dimensionality reduction
intrinsic dimensionality
neighborhood
preserving
Opis:
In this work, we revisit the Locally Linear Embedding (LLE) algorithm that is widely employed in dimensionality reduction. With a particular interest to the correspondences of the nearest neighbors in the original and embedded spaces, we observe that, when prescribing low-dimensional embedding spaces, LLE remains merely a weight-preserving rather than a neighborhood-preserving algorithm. Thus, we propose a \neighborhood-preserving ratio" criterion to estimate the minimal intrinsic dimensionality required for neighborhood preservation. We validate its efficiency on sets of synthetic data, including S-curve, Swiss roll, and a dataset of grayscale images.
Źródło:
Computer Science; 2018, 19 (3); 345-356
1508-2806
2300-7036
Pojawia się w:
Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Inclusion and neighborhood properties of certain subclasses of p-valent functions of complex order defined by convolution
Autorzy:
El-Ashwah, R. M.
Aouf, M. K.
El-Deeb, S. M.
Powiązania:
https://bibliotekanauki.pl/articles/747294.pdf
Data publikacji:
2011
Wydawca:
Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
Tematy:
Analytic
\(p\)-valent
\((n,\theta)\)-neighborhood
inclusion relations
Opis:
In this paper we introduce and investigate three new subclasses of \(p\)-valent analytic functions by using the linear operator \(D_{\lambda,p}^m(f*g)(z)\). The various results obtained here for each of these function classes include coefficient bounds, distortion inequalities and associated inclusion relations for \((n,\theta)\)-neighborhoods of subclasses of analytic and multivalent functions with negative coefficients, which are defined by means of a non-homogenous differential equation.
Źródło:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2011, 65, 1
0365-1029
2083-7402
Pojawia się w:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The set chromatic number of a graph
Autorzy:
Chartrand, Gary
Okamoto, Futaba
Rasmussen, Craig
Zhang, Ping
Powiązania:
https://bibliotekanauki.pl/articles/744459.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
neighbor-distinguishing coloring
set coloring
neighborhood color set
Opis:
For a nontrivial connected graph G, let c: V(G)→ N be a vertex coloring of G where adjacent vertices may be colored the same. For a vertex v of G, the neighborhood color set NC(v) is the set of colors of the neighbors of v. The coloring c is called a set coloring if NC(u) ≠ NC(v) for every pair u,v of adjacent vertices of G. The minimum number of colors required of such a coloring is called the set chromatic number χₛ(G) of G. The set chromatic numbers of some well-known classes of graphs are determined and several bounds are established for the set chromatic number of a graph in terms of other graphical parameters.
Źródło:
Discussiones Mathematicae Graph Theory; 2009, 29, 3; 545-561
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Family, school and neighborhood factors moderating the relationship between physical activity and some aspects of mental health in adolescents
Autorzy:
Kleszczewska, Dorota
Mazur, Joanna
Siedlecka, Jadwiga
Powiązania:
https://bibliotekanauki.pl/articles/2161958.pdf
Data publikacji:
2019-07-15
Wydawca:
Instytut Medycyny Pracy im. prof. dra Jerzego Nofera w Łodzi
Tematy:
family
physical activity
environment
adolescents
Mental Health
neighborhood
Opis:
The impact of physical activity on mental health is widely described in literature. Less attention is given to factors which may modify this correlation, except for gender. The aim of this study was to conduct a qualitative assessment of such papers relating to children and young people. Selected papers were evaluated with regard to additional factors related to family, school and neighborhood. Attention was drawn to the definitions of these variables, the methods of analysis, and the content of the discussion. The starting point for this study included 7 systematic reviews published in 2006–2018. A total of 161 full articles described in detail in those reviews, and representing different research patterns, were selected for qualitative analysis. They met the criteria for the type of publication, mental health outcome, the direction of association, and the age group. A supplementary section of this paper contains a review of Polish literature from the Polish Medical Bibliography, and an analysis of national studies and some more recent papers not included in the analyzed reviews. It was demonstrated that 33 papers analyzed environmental variables to a greater degree than the characteristics of the sample. Twenty-three papers containing the results of statistical analyses were considered to be of particular interest. Almost 50% of these included both the socio-economic position of the family and the characteristics of the neighborhood. However, only 1 featured stratification of the sample with regard to contextual environmental variables. The obtained results are of great practical importance. Firstly, development of the research into environmental moderators should be advocated. Secondly, the social context in which adolescents grow up should be taken into account when designing intervention programs. Int J Occup Med Environ Health. 2019;32(4):423–39
Źródło:
International Journal of Occupational Medicine and Environmental Health; 2019, 32, 4; 423-439
1232-1087
1896-494X
Pojawia się w:
International Journal of Occupational Medicine and Environmental Health
Dostawca treści:
Biblioteka Nauki
Artykuł
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