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