Dominating Set Counting in Graph Classes

  • Shuji Kijima
  • Yoshio Okamoto
  • Takeaki Uno
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6842)


We make an attempt to understand the dominating set counting problem in graph classes from the viewpoint of polynomial-time computability. We give polynomial-time algorithms to count the number of dominating sets (and minimum dominating sets) in interval graphs and trapezoid graphs. They are based on dynamic programming. With the help of dynamic update on a binary tree, we further reduce the time complexity. On the other hand, we prove that counting the number of dominating sets (and minimum dominating sets) in split graphs and chordal bipartite graphs is #P-complete. These results are in vivid contrast with the recent results on counting the independent sets and the matchings in chordal graphs and chordal bipartite graphs.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Shuji Kijima
    • 1
  • Yoshio Okamoto
    • 2
  • Takeaki Uno
    • 3
  1. 1.Graduate School of Information Science and Electrical EngineeringKyushu UniversityJapan
  2. 2.Center for Graduate Education InitiativeJapan Advanced Institute of Science and TechnologyJapan
  3. 3.National Institute of InformaticsJapan

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