FPT results for signed domination

  • Authors:

  • Ying Zheng;Jianxin Wang;Qilong Feng;Jianer Chen

  • Affiliations:

  • School of Information Science and Engineering, Central South University, Changsha, P.R. China;School of Information Science and Engineering, Central South University, Changsha, P.R. China;School of Information Science and Engineering, Central South University, Changsha, P.R. China;School of Information Science and Engineering, Central South University, Changsha, P.R. China,Department of Computer Science and Engineering, Texas A&M University, College Station, Texas

  • Venue:
  • TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
  • Year:
  • 2012

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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.