Geodesic
Total and paired domination stability in prisms
Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 4, pp. 1147-1169

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A set D of vertices in an isolate-free graph is a total dominating set if every vertex is adjacent to a vertex in D. If the set D has the additional property that the subgraph induced by D contains a perfect matching, then D is a paired dominating set of G. The total domination number γ_t(G) and the paired domination number γ_pr(G) of a graph G are the minimum cardinalities of a total dominating set and a paired dominating set of G, respectively. The total domination stability (respectively, paired domination stability) of G, denoted st_γ_t(G) (respectively, st_γ_pr(G)), is the minimum size of a non-isolating set of vertices in G whose removal changes the total domination number (respectively, paired domination number). In this paper, we study total and paired domination stability in prisms.
Keywords: total domination stability, paired domination stability, prism, hypercube 
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     title = {Total and paired domination stability in prisms},
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Gorzkowska, Aleksandra; Henning, Michael A.; Pilśniak, Monika; Tumidajewicz, Elżbieta. Total and paired domination stability in prisms. Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 4, pp. 1147-1169. http://geodesic.mathdoc.fr/item/DMGT_2023_43_4_a14/