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In a graph G, a vertex dominates itself and its neighbors. A subset S ⊆ V(G) is a double dominating set of G if S dominates every vertex of G at least twice. The minimum cardinality of a double dominating set of G is the double domination number $γ_{×2}(G)$. If G ≠ C₅ is a connected graph of order n with minimum degree at least 2, then we show that $γ_{×2}(G) ≤ 3n/4$ and we characterize those graphs achieving equality.
Słowa kluczowe
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
13-28
Opis fizyczny
Daty
wydano
2005
otrzymano
2003-08-25
poprawiono
2004-05-20
Twórcy
autor
- School of Mathematics, Statistics, &, Information Technology, University of KwaZulu-Natal, Pietermaritzburg, 3209 South Africa
Bibliografia
- [1] M. Blidia, M. Chellali, and T.W. Haynes, Characterizations of trees with equal paired and double domination numbers, submitted for publication.
- [2] M. Blidia, M. Chellali, T.W. Haynes and M.A. Henning, Independent and double domination in trees, Utilitas Math., to appear.
- [3] M. Chellali and T.W. Haynes, Paired and double domination in graphs, Utilitas Math., to appear.
- [4] J. Harant and M.A Henning, On double domination in graphs, Discuss. Math. Graph Theory, to appear, doi: 10.7151/dmgt.1256.
- [5] F. Harary and T.W. Haynes, Double domination in graphs, Ars Combin. 55 (2000) 201-213.
- [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.S. Liao and G.J. Chang, Algorithmic aspects of k-tuple domination in graphs, Taiwanese J. Math. 6 (2002) 415-420.
- [9] C.S. Liao and G.J. Chang, k-tuple domination in graphs, Information Processing Letters 87 (2003) 45-50, doi: 10.1016/S0020-0190(03)00233-3.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1255