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Critical Paired Dominating Sets and Irreducible Decompositions of Powers of Edge Ideals
Nguyen Thi Dung
,
Nguyen Thi Thanh Tam
,
Hoang Le Truong
,
Hoang Ngoc Yen
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 $G$.