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2013 | 33 | 4 | 649-656
Tytuł artykułu

Some Sharp Bounds on the Negative Decision Number of Graphs

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let G = (V,E) be a graph. A function f : V → {-1,1} is called a bad function of G if ∑u∈NG(v) f(u) ≤ 1 for all v ∈ V where NG(v) denotes the set of neighbors of v in G. The negative decision number of G, introduced in [12], is the maximum value of ∑v∈V f(v) taken over all bad functions of G. In this paper, we present sharp upper bounds on the negative decision number of a graph in terms of its order, minimum degree, and maximum degree. We also establish a sharp Nordhaus-Gaddum-type inequality for the negative decision number.
Wydawca
Rocznik
Tom
33
Numer
4
Strony
649-656
Opis fizyczny
Daty
wydano
2013-09-01
online
2013-10-15
Twórcy
autor
Bibliografia
  • [1] W. Chen and E. Song, Lower bounds on several versions of signed domination number , Discrete Math. 308 (2008) 1837-1846. doi:10.1016/j.disc.2006.09.050[WoS][Crossref]
  • [2] R. Diestel, Graph Theory (Fourth Edition, Springer-Verlag, 2010).
  • [3] J.E. Dunbar, S.T. Hedetniemi, M.A. Henning and P.J. Slater, Signed domination in graphs, Graph Theory, Combinatorics, and Applications 1 (1995) 311-322.
  • [4] O. Favaron, Signed domination in regular graphs, Discrete Math. 158 (1996) 287-293. doi:10.1016/0012-365X(96)00026-X[Crossref]
  • [5] Z. Füredi and D. Mubayi, Signed domination in regular graphs and set-systems, J. Combin. Theory (B) 76 (1999) 223-239. doi:10.1006/jctb.1999.1905[Crossref]
  • [6] F. Harary, Graph Theory (Addison-Wesley, 1969).
  • [7] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in Graphs: Advanced Topics (Marcel Dekker, 1998).
  • [8] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, 1998).
  • [9] M.A. Henning, Signed total domination in graphs, Discrete Math. 278 (2004) 109-125. doi:10.1016/j.disc.2003.06.002[Crossref]
  • [10] J. Matouˇsek, On the signed domination in graphs, Combinatorica 20 (2000) 103-108. doi:10.1007/s004930070034[Crossref]
  • [11] L. Volkmann, Signed domination and signed domatic numbers of digraphs, Discuss. Math. Graph Theory 31 (2011) 415-427. doi:10.7151/dmgt.1555[Crossref]
  • [12] C. Wang, The negative decision number in graphs, Australas. J. Combin. 41 (2008) 263-272.
  • [13] C. Wang, The signed matchings in graphs, Discuss. Math. Graph Theory 28 (2008) 477-486. doi:10.7151/dmgt.1421[Crossref]
  • [14] C. Wang, Lower negative decision number in a graph, J. Appl. Math. Comput. 34 (2010) 373-384. doi:10.1007/s12190-009-0327-5[Crossref]
  • [15] C. Wang, Voting ‘against’ in regular and nearly regular graphs, Appl. Anal. Discrete Math. 4 (2010) 207-218. doi:10.2298/AADM100213014W[Crossref][WoS]
  • [16] B. Zelinka, Signed total domination number of a graph, Czechoslovak Math. J. 51 (2001) 225-229. doi:10.1023/A:1013782511179[Crossref]
  • [17] Z. Zhang, B. Xu, Y. Li and L. Liu, A note on the lower bounds of signed domination number of a graph, Discrete Math. 195 (1999) 295-298. doi:0.1016/S0012-365X(98)00189-7
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1683
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