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

Acta Mathematica Vietnamica - Tập 44 - Trang 587-601 - 2018
Nguyen Thi Dung1, Nguyen Thi Thanh Tam2, Hoang Le Truong3,4, Hoang Ngoc Yen5
1Thai Nguyen University of Agriculture and Forestry, Thai Nguyen, Vietnam
2 Hung Vuong University, Viet Tri, Vietnam
3Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, Vietnam
4Mathematik und Informatik, Universität des Saarlandes, Saarbrücken, Germany
5Thai Nguyen University of Education, Thai Nguyen, Vietnam

Tóm tắt

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.

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