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## Discussiones Mathematicae Graph Theory

2006 | 26 | 1 | 5-18
Tytuł artykułu

### Algorithmic aspects of total-subdomination in graphs

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let G = (V,E) be a graph and let k ∈ Z⁺. A total k-subdominating function is a function f: V → {-1,1} such that for at least k vertices v of G, the sum of the function values of f in the open neighborhood of v is positive. The total k-subdomination number of G is the minimum value of f(V) over all total k-subdominating functions f of G where f(V) denotes the sum of the function values assigned to the vertices under f. In this paper, we present a cubic time algorithm to compute the total k-subdomination number of a tree and also show that the associated decision problem is NP-complete for general graphs.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
5-18
Opis fizyczny
Daty
wydano
2006
otrzymano
2003-09-15
poprawiono
2005-08-24
Twórcy
autor
• School of Mathematical Sciences, University of KwaZulu-Natal, Pietermaritzburg, 3209 South Africa
autor
• Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303-3083 USA
autor
• School of Mathematical Sciences, University of KwaZulu-Natal, Pietermaritzburg, 3209 South Africa
Bibliografia
• [1] L.W. Beineke and M.A. Henning, Opinion function on trees, Discrete Math. 167-168 (1997) 127-139, doi: 10.1016/S0012-365X(96)00221-X.
• [2] I. Broere, J.H. Hattingh, M.A. Henning and A.A. McRae, Majority domination in graphs, Discrete Math. 138 (1995) 125-135, doi: 10.1016/0012-365X(94)00194-N.
• [3] G. Chang, S.C. Liaw and H.G. Yeh, k-subdomination in graphs, Discrete Applied Math. 120 (2002) 55-60, doi: 10.1016/S0166-218X(01)00280-3.
• [4] E.J. Cockayne and C. Mynhardt, On a generalisation of signed dominating functions of graphs, Ars Combin. 43 (1996) 235-245.
• [5] J.E. Dunbar, S.T. Hedetniemi, M.A. Henning and P.J. Slater, Signed domination in graphs, Graph Theory, Combinatorics and Applications, John Wiley & Sons, Inc. 1 (1995) 311-322.
• [6] O. Favaron, Signed domination in regular graphs, Discrete Math. 158 (1996) 287-293, doi: 10.1016/0012-365X(96)00026-X.
• [7] Z. Furedi 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.
• [8] M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness (Freeman, New York, 1979).
• [9] L. Harris and J.H. Hattingh, The algorithmic complexity of certain functional variations of total domination in graphs, Australasian J. Combin. 29 (2004) 143-156.
• [10] L. Harris, J.H. Hattingh and M.A. Henning, Total k-subdominating functions on graphs, submitted for publication.
• [11] J.H. Hattingh, M.A. Henning and P.J. Slater, The algorithmic complexity of signed domination in graphs, Australasian J. Combin. 12 (1995) 101-112.
• [12] M.A. Henning, Domination in regular graphs, Ars Combin. 43 (1996) 263-271.
• [13] M.A. Henning, Dominating functions in graphs, Domination in Graphs: Volume II (Marcel-Dekker, Inc., 1998) 31-62.
• [14] M.A. Henning, Signed total domination in graphs, to appear in Discrete Math.
• [15] M.A. Henning and H. Hind, Strict open majority functions in Graphs, J. Graph Theory 28 (1998) 49-56, doi: 10.1002/(SICI)1097-0118(199805)28:1<49::AID-JGT6>3.0.CO;2-F
• [16] M.A. Henning and P.J. Slater, Inequalities relating domination parameters in cubic graphs, Discrete Math. 158 (1996) 87-98, doi: 10.1016/0012-365X(96)00025-8.
• [17] P. Lam and B. Wei, On the total domination number of graphs, submitted for publication.
• [18] J. Matousek, On the signed domination in graphs, Combinatoria 20 (2000) 103-108, doi: 10.1007/s004930070034.
• [19] X. Yang, X. Huang and Q. Hou, On graphs with equal signed and majority domination number, manuscript (personal communication by X. Yang).
• [20] H. Yeh and G.J. Chang, Algorithmic aspects of majority domination, Taiwanese J. Math. 1 (1997) 343-350.
• [21] B. Zelinka, Some remarks on domination in cubic graphs, Discrete Math. 158 (1996) 249-255, doi: 10.1016/0012-365X(94)00324-C.
• [22] B. Zelinka, Signed total domination number of a graph, Czechoslovak Math. J. 51 (2001) 225-229, doi: 10.1023/A:1013782511179.
• [23] 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: 10.1016/S0012-365X(98)00189-7.
Typ dokumentu
Bibliografia
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