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Acta Mathematica Vietnamica

, Volume 44, Issue 3, pp 587–601 | Cite as

Critical Paired Dominating Sets and Irreducible Decompositions of Powers of Edge Ideals

  • Nguyen Thi Dung
  • Nguyen Thi Thanh Tam
  • Hoang Le TruongEmail author
  • Hoang Ngoc Yen
Article

Abstract

Let G be a finite simple graph. A set S of vertices is a critical paired dominating set of G, if every vertex is adjacent to a vertex in S and the removal of any vertex does not change the matching number of G. In this paper, we give a characterization of graphs G which has a critical paired dominating set in terms of the irreducible decomposition of powers of the edge ideal associated to G.

Keywords

Edge ideals Irreducible ideals Irreducible decomposition Matching Factor-critical graphs Critical paired dominating set 

Mathematics Subject Classification (2010)

13A30 13D45 13E05 13H10 

Notes

Acknowledgements

The authors would like to thank Professor Marcel Morales for his interesting discussions on this subject. The authors would like to thank the referee for the valuable comments to improve this article.

Funding Information

This research was funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.04 − 2017.14.

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Nguyen Thi Dung
    • 1
  • Nguyen Thi Thanh Tam
    • 2
  • Hoang Le Truong
    • 3
    • 4
    Email author
  • Hoang Ngoc Yen
    • 5
  1. 1.Thai Nguyen University of Agriculture and ForestryThai NguyenVietnam
  2. 2.Hung Vuong UniversityViet TriVietnam
  3. 3.Institute of MathematicsVietnam Academy of Science and TechnologyHanoiVietnam
  4. 4.Mathematik und InformatikUniversität des SaarlandesSaarbrückenGermany
  5. 5.Thai Nguyen University of EducationThai NguyenVietnam

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