Geodesic
Paired domination stability in graphs
Ars Mathematica Contemporanea, Tome 22 (2022) no. 2, article no. 04, 18 p.

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A set S of vertices in a graph G is a paired dominating set if every vertex of G is adjacent to a vertex in S and the subgraph induced by S contains a perfect matching (not necessarily as an induced subgraph). The paired domination number, γpr(G), of G is the minimum cardinality of a paired dominating set of G. A set of vertices whose removal from G produces a graph without isolated vertices is called a non-isolating set. The minimum cardinality of a non-isolating set of vertices whose removal decreases the paired domination number is the γpr−-stability of G, denoted stγpr−(G). The paired domination stability of G is the minimum cardinality of a non-isolating set of vertices in G whose removal changes the paired domination number. We establish properties of paired domination stability in graphs. We prove that if G is a connected graph with γpr(G) ≥ 4, then stγpr−(G) ≤ 2Δ(G) where Δ(G) is the maximum degree in G, and we characterize the infinite family of trees that achieve equality in this upper bound. 
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Aleksandra Gorzkowska; Michael A. Henning; Monika Pilśniak; Elżbieta Tumidajewicz. Paired domination stability in graphs. Ars Mathematica Contemporanea, Tome 22 (2022) no. 2, article  no. 04, 18 p. doi : 10.26493/1855-3974.2522.eb3. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2522.eb3/

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