Czechoslovak Mathematical Journal

, Volume 59, Issue 1, pp 95–100 | Cite as

Weakly connected domination stable trees

  • Magdalena Lemańska
  • Joanna Raczek


A dominating set D ⊆ V(G) is a weakly connected dominating set in G if the subgraph G[D] w = (N G [D], E w ) weakly induced by D is connected, where E w is the set of all edges having at least one vertex in D. Weakly connected domination number γw (G) of a graph G is the minimum cardinality among all weakly connected dominating sets in G. A graph G is said to be weakly connected domination stable or just γw -stable if γw (G) = γ w (G + e) for every edge e belonging to the complement Ḡ of G. We provide a constructive characterization of weakly connected domination stable trees.


weakly connected domination number tree stable graphs 

MSC 2000

05C05 05C69 


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  1. [1]
    D. P. Sumner, P. Blitch: Domination critical graphs. J. Combin. Theory Ser. B 34 (1983), 65–76.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    J. E. Dunbar, J. W. Grossman, J. H. Hattingh, S. T. Hedetniemi and A. McRae: On weakly-connected domination in graphs. Discrete Mathematics 167–168 (1997), 261–269.CrossRefMathSciNetGoogle Scholar
  3. [3]
    M. A. Henning: Total domination excellent trees. Discrete Mathematics 263 (2003), 93–104.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    X. Chen, L. Sun and D. Ma: Connected domination critical graphs. Applied Mathematics Letters 17 (2004), 503–507.zbMATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    M. Lemańska: Domination numbers in graphs with removed edge or set of edges. 25 (2005), 51–56.zbMATHGoogle Scholar

Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2009

Authors and Affiliations

  1. 1.Department of Applied Physics and MathematicsGdańsk University of TechnologyGdańskPoland

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