Wyniki wyszukiwania dla: ROMAN DOMINATION NUMBER WEAKLY CONNECTED SET WEAKLY CONNECTED ROMAN DOMINATION NUMBER TREES

• Weakly connected Roman domination in graphs

  Publikacja

  • J. Raczek
  • J. Cyman

  - DISCRETE APPLIED MATHEMATICS - Rok 2019

  A Roman dominating function on a graph G=(V,E) is defined to be a function f :V → {0,1,2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v)=2. A dominating set D⊆V is a weakly connected dominating set of G if the graph (V,E∩(D×V)) is connected. We define a weakly connected Roman dominating function on a graph G to be a Roman dominating function such that the set...

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• Progress on Roman and Weakly Connected Roman Graphs

  Publikacja

  • J. Raczek
  • R. Zuazua

  - Mathematics - Rok 2021

  A graph G for which γR(G)=2γ(G) is the Roman graph, and if γwcR(G)=2γwc(G), then G is the weakly connected Roman graph. In this paper, we show that the decision problem of whether a bipartite graph is Roman is a co-NP-hard problem. Next, we prove similar results for weakly connected Roman graphs. We also study Roman trees improving the result of M.A. Henning’s A characterization of Roman trees, Discuss. Math. Graph Theory 22 (2002)....

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• Similarities and Differences Between the Vertex Cover Number and the Weakly Connected Domination Number of a Graph

  Publikacja

  • M. Lemańska
  • J. A. RODRíGUEZ-VELáZQUEZ
  • R. Trujillo-Rasua

  - FUNDAMENTA INFORMATICAE - Rok 2017

  A vertex cover of a graph G = (V, E) is a set X ⊂ V such that each edge of G is incident to at least one vertex of X. The ve cardinality of a vertex cover of G. A dominating set D ⊆ V is a weakly connected dominating set of G if the subgraph G[D]w = (N[D], Ew) weakly induced by D, is connected, where Ew is the set of all edges having at least one vertex in D. The weakly connected domination number γw(G) of G is the minimum cardinality...

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• Lower bound on the weakly connected domination number of a tree

  Publikacja

  • M. Lemańska

  - Australasian Journal of Combinatorics - Rok 2007

  Praca dotyczy dolnego ograniczenia liczby dominowania słabo spójnego w drzewach (ograniczenie ze względu na ilość wierzchołków i ilość wierzchołków końcowych w drzewie).

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• On the connected and weakly convex domination numbers

  Publikacja

  • M. Lemańska
  • M. Dettlaff
  • D. Osula
  • M. J. Souto Salorio

  - Journal of Combinatorial Mathematics and Combinatorial Computing - Rok 2020

  In this paper we study relations between connected and weakly convex domination numbers. We show that in general the difference between these numbers can be arbitrarily large and we focus on the graphs for which a weakly convex domination number equals a connected domination number. We also study the influence of the edge removing on the weakly convex domination number, in particular we show that a weakly convex domination number...

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• Some variants of perfect graphs related to the matching number, the vertex cover and the weakly connected domination number

  Publikacja

  • S. Bermudo
  • M. Dettlaff
  • M. Lemańska

  - DISCRETE APPLIED MATHEMATICS - Rok 2021

  Given two types of graph theoretical parameters ρ and σ, we say that a graph G is (σ, ρ)- perfect if σ(H) = ρ(H) for every non-trivial connected induced subgraph H of G. In this work we characterize (γw, τ )-perfect graphs, (γw, α′)-perfect graphs, and (α′, τ )-perfect graphs, where γw(G), τ (G) and α′(G) denote the weakly connected domination number, the vertex cover number and the matching number of G, respectively. Moreover,...

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• Weakly connected domination stable trees [online]

  Publikacja

  • M. Lemańska
  • J. Raczek

  - CZECHOSLOVAK MATHEMATICAL JOURNAL - Rok 2009

  Praca dotyczy pełnej charakteryzacji drzew stabilnych ze względu na liczbę dominowania słabo spójnego.

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• Weakly convex domination subdivision number of a graph

  Publikacja

  • M. Dettlaff
  • S. Kosary
  • M. Lemańska
  • S. Sheikholeslami

  - FILOMAT - Rok 2016

  A set X is weakly convex in G if for any two vertices a; b \in X there exists an ab–geodesic such that all of its vertices belong to X. A set X \subset V is a weakly convex dominating set if X is weakly convex and dominating. The weakly convex domination number \gamma_wcon(G) of a graph G equals the minimum cardinality of a weakly convex dominating set in G. The weakly convex domination subdivision number sd_wcon (G) is the minimum...

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• Weakly connected domination subdivision numbers

  Publikacja

  • J. Raczek

  - Discussiones Mathematicae Graph Theory - Rok 2008

  Liczba podziału krawędzi dla dominowania słabo spójnego to najmniejsza liczba krawędzi jaką należy podzielić, aby wzrosła liczba dominowania słabo wypukłego. W pracy przedstawione są własności liczby podziału krawędzi dla dominowania słabo spójnego dla różnych grafów.

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• Weakly connected domination critical graphs

  Publikacja

  • M. Lemańska
  • A. Patyk-Łońska

  - Opuscula Mathematica - Rok 2008

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

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