# FPT Results for Signed Domination

• Ying Zheng
• Jianxin Wang
• Qilong Feng
• Jianer Chen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7287)

## Abstract

A function f:v → { − 1, + 1} defined on the vertices of a graph G is a signed dominating function if the sum of its function values over any closed neighborhood is at least one. The weight of a signed dominating function is f(V) = ∑ f(v), over all vertices v ∈ V. The signed domination number of a graph G, denoted by γ s (G), equals the minimum weight of a signed dominating function of G. The decision problem corresponding to the problem of computing γ s is an important NP-complete problem derived from social network. A signed dominating set is a set of vertices assigned the value + 1 under the function f in the graph. In this paper, we give some fixed parameter tractable results for signed dominating set problem, specifically the kernels for signed dominating set problem on general and special graphs. These results generalize the parameterized algorithm for this problem. Furthermore we propose a parameterized algorithm for signed dominating set problem on planar graphs.

## Keywords

Bipartite Graph Planar Graph Tree Decomposition Domination Number Chordal Graph
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

1. 1.
Dunbar, J., Hedetniemi, S., Henning, M., Slater, P.: Signed domination in graphs. Graph Theory, Combinatorics and Applications, 311–322 (1995)Google Scholar
2. 2.
Hattingh, J., Henning, M., Slater, P.: The algorithmic complexity of signed domination in graphs. Australasian Journal of Combinatorics 12, 101–112 (1995)
3. 3.
Hass, R., Wexler, T.: Signed domination numbers of a graph and its complement. Discrete Math. 283, 87–92 (2004)
4. 4.
Zelinka, B.: Signed total domination number of a graph. Czechoslovak Math. 51, 225–229 (2001)
5. 5.
Matousek, J.: On the signed domination in graphs. Combinatorica 20, 103–108 (2000)
6. 6.
Robertson, N., Seymour, P.D.: Graph minors X. Obstructions to tree decomposition. J. of Combinatorial Theory, Series B 52, 153–190 (1991)
7. 7.
Zhang, Z., Xu, B., Li, Y., Liu, L.: A note on the lower bounds of signed domination number of a graph. Discrete Math. 195, 295–298 (1999)
8. 8.
Favaron, O.: Signed domination in regular graphs. Discrete Math. 158, 287–293 (1996)
9. 9.
Kloks, T. (ed.): Treewidth: Computations and Approximations. LNCS, vol. 842. Springer, Heidelberg (1994)
10. 10.
Bodlaender, H.L.: Treewidth: Algorithmic Techniques and Results. In: Privara, I., Ružička, P. (eds.) MFCS 1997. LNCS, vol. 1295, pp. 19–36. Springer, Heidelberg (1997)
11. 11.
Henning, M.A., Slater, P.J.: Irregularities relating domination parameters in cubic graphs. Discrete Mathematics 158, 87–98 (1996)
12. 12.
Henning, M.A.: Domination in regular graphs. Ars Combinatoria 43, 263–271 (1996)
13. 13.
Demaine, E.D., Fomin, F.V., Thilikos, D.M.: Bidimensional parameters and local treewidth. SIAM J. Disc. Math. 18(3), 501–511 (2004)
14. 14.
Alber, J., Fellows, M., Niedermeier, R.: Polynomial time data reduction for dominating set. J. ACM 51, 363–384 (2004)

## Authors and Affiliations

• Ying Zheng
• 1
• Jianxin Wang
• 1
• Qilong Feng
• 1
• Jianer Chen
• 1
• 2
1. 1.School of Information Science and EngineeringCentral South UniversityChangshaP.R. China
2. 2.Department of Computer Science and EngineeringTexas A&M UniversityCollege StationUSA