Critical Paired Dominating Sets and Irreducible Decompositions of Powers of Edge Ideals
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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.
KeywordsEdge ideals Irreducible ideals Irreducible decomposition Matching Factor-critical graphs Critical paired dominating set
Mathematics Subject Classification (2010)13A30 13D45 13E05 13H10
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.
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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