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2007 | 27 | 1 | 93-103
Tytuł artykułu

Characterization of block graphs with equal 2-domination number and domination number plus one

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let G be a simple graph, and let p be a positive integer. A subset D ⊆ V(G) is a p-dominating set of the graph G, if every vertex v ∈ V(G)-D is adjacent with at least p vertices of D. The p-domination number γₚ(G) is the minimum cardinality among the p-dominating sets of G. Note that the 1-domination number γ₁(G) is the usual domination number γ(G).
If G is a nontrivial connected block graph, then we show that γ₂(G) ≥ γ(G)+1, and we characterize all connected block graphs with γ₂(G) = γ(G)+1. Our results generalize those of Volkmann [12] for trees.
Słowa kluczowe
Wydawca
Rocznik
Tom
27
Numer
1
Strony
93-103
Opis fizyczny
Daty
wydano
2007
otrzymano
2005-12-07
poprawiono
2006-10-18
Twórcy
  • Lehrstuhl II für Mathematik, RWTH Aachen University, 52056 Aachen, Germany
  • Lehrstuhl II für Mathematik, RWTH Aachen University, 52056 Aachen, Germany
Bibliografia
  • [1] M. Blidia, M. Chellali and L. Volkmann, Bounds of the 2-domination number of graphs, Utilitas Math. 71 (2006) 209-216.
  • [2] J.F. Fink and M.S. Jacobson, n-domination in graphs, in: Graph Theory with Applications to Algorithms and Computer Science (John Wiley and Sons, New York, 1985), 282-300.
  • [3] J.F. Fink and M.S. Jacobson, On n-domination, n-dependence and forbidden subgraphs, in: Graph Theory with Applications to Algorithms and Computer Science (John Wiley and Sons, New York, 1985), 301-311.
  • [4] J.F. Fink, M.S. Jacobson, L.F. Kinch and J. Roberts, On graphs having domination number half their order, Period. Math. Hungar. 16 (1985) 287-293, doi: 10.1007/BF01848079.
  • [5] T. Gallai, Über extreme Punkt-und Kantenmengen, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 2 (1959) 133-138.
  • [6] T.W. Haynes, S.T. Hedetniemi, and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998).
  • [7] T.W. Haynes, S.T. Hedetniemi, and P.J. Slater (eds.), Domination in Graphs: Advanced Topics (Marcel Dekker, New York, 1998).
  • [8] C. Payan and N.H. Xuong, Domination-balanced graphs, J. Graph Theory 6 (1982) 23-32, doi: 10.1002/jgt.3190060104.
  • [9] B. Randerath and L. Volkmann, Characterization of graphs with equal domination and covering number, Discrete Math. 191 (1998) 159-169, doi: 10.1016/S0012-365X(98)00103-4.
  • [10] J. Topp and L. Volkmann, On domination and independence numbers of graphs, Results Math. 17 (1990) 333-341.
  • [11] L. Volkmann, Foundations of Graph Theory (Springer, Wien, New York, 1996) (in German).
  • [12] L. Volkmann, Some remarks on lower bounds on the p-domination number in trees, J. Combin. Math. Combin. Comput., to appear.
  • [13] B. Xu, E.J. Cockayne, T.W. Haynes, S.T. Hedetniemi and S. Zhou, Extremal graphs for inequalities involving domination parameters, Discrete Math. 216 (2000) 1-10, doi: 10.1016/S0012-365X(99)00251-4.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1347
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