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2009 | 29 | 1 | 71-86
Tytuł artykułu

Restrained domination in unicyclic graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let G = (V,E) be a graph. A set S ⊆ V is a restrained dominating set if every vertex in V-S is adjacent to a vertex in S and to a vertex in V-S. The restrained domination number of G, denoted by $γ_r(G)$, is the minimum cardinality of a restrained dominating set of G. A unicyclic graph is a connected graph that contains precisely one cycle. We show that if U is a unicyclic graph of order n, then $γ_r(U) ≥ ⎡n/3⎤$, and provide a characterization of graphs achieving this bound.
Słowa kluczowe
Wydawca
Rocznik
Tom
29
Numer
1
Strony
71-86
Opis fizyczny
Daty
wydano
2009
otrzymano
2007-11-08
poprawiono
2008-10-06
zaakceptowano
2008-10-06
Twórcy
  • Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303-3083, USA
  • Department of Mathematics, University of Johannesburg, P.O. Box 524, Auckland Park 2006, South Africa
  • Department of Mathematics, University of Tennessee, Chattanooga, 615 McCallie Avenue, Chattanooga, TN 37403, USA
  • Department of Linguistics, The Ohio State University, 222 Oxley Hall, 1712 Neil Avenue, Columbus, OH 43210, USA
  • Department of Mathematics, University of Tennessee, Chattanooga, 615 McCallie Avenue, Chattanooga, TN 37403, USA
Bibliografia
  • [1] G. Chartrand and L. Lesniak, Graphs & Digraphs: Fourth Edition (Chapman & Hall, Boca Raton, FL, 2005).
  • [2] P. Dankelmann, D. Day, J.H. Hattingh, M.A. Henning, L.R. Markus and H.C. Swart, On equality in an upper bound for the restrained and total domination numbers of a graph, to appear in Discrete Math.
  • [3] P. Dankelmann, J.H. Hattingh, M.A. Henning and H.C. Swart, Trees with equal domination and restrained domination numbers, J. Global Optim. 34 (2006) 597-607, doi: 10.1007/s10898-005-8565-z.
  • [4] G.S. Domke, J.H. Hattingh, S.T. Hedetniemi and L.R. Markus, Restrained domination in trees, Discrete Math. 211 (2000) 1-9, doi: 10.1016/S0012-365X(99)00036-9.
  • [5] G.S. Domke, J.H. Hattingh, M.A. Henning and L.R. Markus, Restrained domination in graphs with minimum degree two, J. Combin. Math. Combin. Comput. 35 (2000) 239-254.
  • [6] G.S. Domke, J.H. Hattingh, S.T. Hedetniemi, R.C. Laskar and L.R. Markus, Restrained domination in graphs, Discrete Math. 203 (1999) 61-69, doi: 10.1016/S0012-365X(99)00016-3.
  • [7] J.H. Hattingh and M.A. Henning, Restrained domination excellent trees, Ars Combin. 87 (2008) 337-351.
  • [8] J.H. Hattingh, E. Jonck, E. J. Joubert and A.R. Plummer, Nordhaus-Gaddum results for restrained domination and total restrained domination in graphs, Discrete Math. 308 (2008) 1080-1087, doi: 10.1016/j.disc.2007.03.061.
  • [9] J.H. Hattingh and A.R. Plummer, A note on restrained domination in trees, to appear in Ars Combin.
  • [10] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1997).
  • [11] T.W. Haynes, S.T. Hedetniemi and P.J. Slater (eds), Domination in Graphs: Advanced Topics (Marcel Dekker, New York, 1997).
  • [12] M.A. Henning, Graphs with large restrained domination number, Discrete Math. 197/198 (1999) 415-429, doi: 10.1016/S0012-365X(99)90095-X.
  • [13] B. Zelinka, Remarks on restrained and total restrained domination in graphs, Czechoslovak Math. J. 55 (130) (2005) 393-396, doi: 10.1007/s10587-005-0029-6.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1433
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