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Labelling algorithms for paired-domination problems in block and interval graphs

Author

Listed:
  • Lei Chen

    (East China Normal University)

  • Changhong Lu

    (East China Normal University
    East China Normal University)

  • Zhenbing Zeng

    (East China Normal University)

Abstract

Let G=(V,E) be a graph without isolated vertices. A set S⊆V is a paired-dominating set if every vertex in V−S is adjacent to a vertex in S and the subgraph induced by S contains a perfect matching. The paired-domination problem is to determine the paired-domination number, which is the minimum cardinality of a paired-dominating set. Motivated by a mistaken algorithm given by Chen, Kang and Ng (Discrete Appl. Math. 155:2077–2086, 2007), we present two linear time algorithms to find a minimum cardinality paired-dominating set in block and interval graphs. In addition, we prove that paired-domination problem is NP-complete for bipartite graphs, chordal graphs, even for split graphs.

Suggested Citation

  • Lei Chen & Changhong Lu & Zhenbing Zeng, 2010. "Labelling algorithms for paired-domination problems in block and interval graphs," Journal of Combinatorial Optimization, Springer, vol. 19(4), pages 457-470, May.
    • Handle: RePEc:spr:jcomop:v:19:y:2010:i:4:d:10.1007_s10878-008-9177-6
    DOI: 10.1007/s10878-008-9177-6
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    References listed on IDEAS

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    1. Michael A. Henning, 2007. "Graphs with large paired-domination number," Journal of Combinatorial Optimization, Springer, vol. 13(1), pages 61-78, January.
    2. Paul Dorbec & Sylvain Gravier & Michael A. Henning, 2007. "Paired-domination in generalized claw-free graphs," Journal of Combinatorial Optimization, Springer, vol. 14(1), pages 1-7, July.
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    Cited by:

    1. Hao Chen & Zihan Lei & Tian Liu & Ziyang Tang & Chaoyi Wang & Ke Xu, 2016. "Complexity of domination, hamiltonicity and treewidth for tree convex bipartite graphs," Journal of Combinatorial Optimization, Springer, vol. 32(1), pages 95-110, July.
    2. Changhong Lu & Qingjie Ye & Chengru Zhu, 2022. "Algorithmic aspect on the minimum (weighted) doubly resolving set problem of graphs," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 2029-2039, October.
    3. D. Pradhan & Anupriya Jha, 2018. "On computing a minimum secure dominating set in block graphs," Journal of Combinatorial Optimization, Springer, vol. 35(2), pages 613-631, February.
    4. Changhong Lu & Qingjie Ye & Chengru Zhu, 0. "Algorithmic aspect on the minimum (weighted) doubly resolving set problem of graphs," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-11.
    5. Chao Wang & Lei Chen & Changhong Lu, 2016. "$$k$$ k -Power domination in block graphs," Journal of Combinatorial Optimization, Springer, vol. 31(2), pages 865-873, February.
    6. Yancai Zhao & Erfang Shan, 2016. "An efficient algorithm for distance total domination in block graphs," Journal of Combinatorial Optimization, Springer, vol. 31(1), pages 372-381, January.
    7. Ching-Chi Lin & Cheng-Yu Hsieh & Ta-Yu Mu, 2022. "A linear-time algorithm for weighted paired-domination on block graphs," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 269-286, August.

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