### Abstract

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.

Original language | English |
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Title of host publication | Computing and Combinatorics - 17th Annual International Conference, COCOON 2011, Proceedings |

Pages | 13-24 |

Number of pages | 12 |

DOIs | |

Publication status | Published - Aug 29 2011 |

Event | 17th Annual International Computing and Combinatorics Conference, COCOON 2011 - Dallas, TX, United States Duration: Aug 14 2011 → Aug 16 2011 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 6842 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 17th Annual International Computing and Combinatorics Conference, COCOON 2011 |
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Country | United States |

City | Dallas, TX |

Period | 8/14/11 → 8/16/11 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Computing and Combinatorics - 17th Annual International Conference, COCOON 2011, Proceedings*(pp. 13-24). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6842 LNCS). https://doi.org/10.1007/978-3-642-22685-4_2

**Dominating set counting in graph classes.** / Kijima, Shuji; Okamoto, Yoshio; Uno, Takeaki.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Computing and Combinatorics - 17th Annual International Conference, COCOON 2011, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6842 LNCS, pp. 13-24, 17th Annual International Computing and Combinatorics Conference, COCOON 2011, Dallas, TX, United States, 8/14/11. https://doi.org/10.1007/978-3-642-22685-4_2

}

TY - GEN

T1 - Dominating set counting in graph classes

AU - Kijima, Shuji

AU - Okamoto, Yoshio

AU - Uno, Takeaki

PY - 2011/8/29

Y1 - 2011/8/29

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=80051982070&partnerID=8YFLogxK

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U2 - 10.1007/978-3-642-22685-4_2

DO - 10.1007/978-3-642-22685-4_2

M3 - Conference contribution

AN - SCOPUS:80051982070

SN - 9783642226847

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 13

EP - 24

BT - Computing and Combinatorics - 17th Annual International Conference, COCOON 2011, Proceedings

ER -