Geodesic
On graphs with a unique minimum hull set
Discussiones Mathematicae. Graph Theory, Tome 21 (2001) no. 1, pp. 31-42

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We show that for every integer k ≥ 2 and every k graphs G₁,G₂,...,Gₖ, there exists a hull graph with k hull vertices v₁,v₂,...,vₖ such that link L(v_i) = G_i for 1 ≤ i ≤ k. Moreover, every pair a, b of integers with 2 ≤ a ≤ b is realizable as the hull number and geodetic number (or upper geodetic number) of a hull graph. We also show that every pair a,b of integers with a ≥ 2 and b ≥ 0 is realizable as the hull number and forcing geodetic number of a hull graph.
Keywords: geodetic set, geodetic number, convex hull, hull set, hull number, hull graph 
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Chartrand, Gary; Zhang, Ping. On graphs with a unique minimum hull set. Discussiones Mathematicae. Graph Theory, Tome 21 (2001) no. 1, pp. 31-42. http://geodesic.mathdoc.fr/item/DMGT_2001_21_1_a2/