Year 2019

• Graphs with equal domination and certified domination numbers

  Publication

  • M. Dettlaff
  • M. Lemańska
  • J. Topp
  • M. Miotk
  • R. Ziemann
  • P. Żyliński

  - Opuscula Mathematica - Year 2019

  A setDof vertices of a graphG= (VG,EG) is a dominating set ofGif every vertexinVG−Dis adjacent to at least one vertex inD. The domination number (upper dominationnumber, respectively) ofG, denoted byγ(G) (Γ(G), respectively), is the cardinality ofa smallest (largest minimal, respectively) dominating set ofG. A subsetD⊆VGis calleda certified dominating set ofGifDis a dominating set ofGand every vertex inDhas eitherzero...

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Year 2018

• On domination multisubdivision number of unicyclic graphs

  Publication

  • J. Raczek

  - Opuscula Mathematica - Year 2018

  The paper continues the interesting study of the domination subdivision number and the domination multisubdivision number. On the basis of the constructive characterization of the trees with the domination subdivision number equal to 3 given in [H. Aram, S.M. Sheikholeslami, O. Favaron, Domination subdivision number of trees, Discrete Math. 309 (2009), 622–628], we constructively characterize all connected unicyclic graphs with...

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Year 2016

• Edge subdivision and edge multisubdivision versus some domination related parameters in generalized corona graphs

  Publication

  • M. Dettlaff
  • J. Raczek
  • I. G. Yero

  - Opuscula Mathematica - Year 2016

  Given a graph G= (V, E), the subdivision of an edge e=uv∈E(G) means the substitution of the edge e by a vertex x and the new edges ux and xv. The domination subdivision number of a graph G is the minimum number of edges of G which must be subdivided (where each edge can be subdivided at most once) in order to increase the domination number. Also, the domination multisubdivision number of G is the minimum number of subdivisions...

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Year 2015

• The paired-domination and the upper paired-domination numbers of graphs

  Publication

  • W. Ulatowski

  - Opuscula Mathematica - Year 2015

  In this paper we obtain the upper bound for the upper paired-domination number and we determine the extremal graphs achieving this bound. Moreover we determine the upper paired- domination number for cycles.

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Year 2014

• A NOTE ON ON-LINE RAMSEY NUMBERS FOR QUADRILATERALS

  Publication

  • J. Cyman
  • T. Dzido

  - Opuscula Mathematica - Year 2014

  We consider on-line Ramsey numbers defined by a game played between two players, Builder and Painter. In each round Builder draws an the edge and Painter colors it either red or blue, as it appears. Builder’s goal is to force Painter to create a monochromatic copy of a fixed graph H in as few rounds as possible. The minimum number of rounds (assuming both players play perfectly) is the on-line Ramsey number \widetilde{r}(H) of...

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• Difference functional inequalities and applications.

  Publication

  • A. Szafrańska

  - Opuscula Mathematica - Year 2014

  The paper deals with the difference inequalities generated by initial boundary value problems for hyperbolic nonlinear differential functional systems. We apply this result to investigate the stability of constructed difference schemes. The proof of the convergence of the difference method is based on the comparison technique, and the result for difference functional inequalities is used. Numerical examples are presented.

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Year 2013

• All graphs with paired-domination number two less than their order

  Publication

  • W. Ulatowski

  - Opuscula Mathematica - Year 2013

  Let G=(V,E) be a graph with no isolated vertices. A set S⊆V is a paired-dominating set of G if every vertex not in S is adjacent with some vertex in S and the subgraph induced by S contains a perfect matching. The paired-domination number γp(G) of G is defined to be the minimum cardinality of a paired-dominating set of G. Let G be a graph of order n. In [Paired-domination in graphs, Networks 32 (1998), 199-206] Haynes and Slater...

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Year 2012

• An upper bound on the total outer-independent domination number of a tree

  Publication

  • M. Krzywkowski

  - Opuscula Mathematica - Year 2012

  A total outer-independent dominating set of a graph G=(V(G),E(G)) is a set D of vertices of G such that every vertex of G has a neighbor in D, and the set V(G)D is independent. The total outer-independent domination number of a graph G, denoted by gamma_t^{oi}(G), is the minimum cardinality of a total outer-independent dominating set of G. We prove that for every tree T of order n >= 4, with l leaves and s support vertices we have...

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• On the hat problem on a graph

  Publication

  • M. Krzywkowski

  - Opuscula Mathematica - Year 2012

  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....

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Year 2008

• The work of Professor Andrzej Lasota on asymptotic stability and recent progress

  Publication

  • W. Bartoszek

  - Opuscula Mathematica - Year 2008

  Praca poświęcona jest wkładowi Profesora Andrzeja Lasoty w teorię asymptotycznej stabilności iteracji operatorów stochastycznych na przestrzeni ostatnich 36 lat. Podkreślono aplikacyjny charakter wyników, pokazując stosowne przykłady z modelowania rozwoju komórki, optymalizacji wierceń geologicznych i ewolucji modeli kwantowych.

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• Weakly connected domination critical graphs

  Publication

  • M. Lemańska
  • A. Patyk-Łońska

  - Opuscula Mathematica - Year 2008

  Praca dotyczy niektórych klas grafów krytycznych ze względu na liczbę dominowania słabo spójnego.

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Year 2004

• NP-completeness of convex and weakly convex domiating set decision problems.

  Publication

  • J. Raczek

  - Opuscula Mathematica - Year 2004

  Liczby dominowania wypukłego i słabo wypukłego są nowymi rodzajami liczb dominowania. W tym artykule pokazujemy, że problemy decyzyjne dominowania wypukłegi i słabo wypukłego są NP-zupełne w przypadku grafów dwudzielnych oraz split grafów. Posługując się zmodyfikowanym algorytmem Washalla możemy w czasie wielomianowym określić, czy dany podzbiór wierzchołków grafu jest spójny bądź słabo spójny.

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