Geodesic
(H,k) stable graphs with minimum size
Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 1, pp. 137-149.

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Let us call a G (H,k) graph vertex stable if it contains a subgraph H ever after removing any of its k vertices. By Q(H,k) we will denote the minimum size of an (H,k) vertex stable graph. In this paper, we are interested in finding Q(₃,k), Q(₄,k), Q(K_1,p,k) and Q(Kₛ,k).
Keywords: graph, stable graph 
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Dudek, Aneta; Szymański, Artur; Zwonek, Małgorzata. (H,k) stable graphs with minimum size. Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 1, pp. 137-149. http://geodesic.mathdoc.fr/item/DMGT_2008_28_1_a9/

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