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Res."],"accepted":{"date-parts":[[2020,8,20]]},"published-print":{"date-parts":[[2021]]},"abstract":"<jats:p>In the geodetic convexity, a set of vertices <jats:italic>S<\/jats:italic> of a graph <jats:italic>G<\/jats:italic> is <jats:italic>convex<\/jats:italic> if all vertices belonging to any shortest path between two vertices of <jats:italic>S<\/jats:italic> lie in <jats:italic>S<\/jats:italic>. The <jats:italic>convex hull<\/jats:italic> <jats:italic>H<\/jats:italic>(<jats:italic>S<\/jats:italic>) of <jats:italic>S<\/jats:italic> is the smallest convex set containing <jats:italic>S<\/jats:italic>. If <jats:italic>H<\/jats:italic>(<jats:italic>S<\/jats:italic>) = <jats:italic>V<\/jats:italic> (<jats:italic>G<\/jats:italic>), then <jats:italic>S<\/jats:italic> is a <jats:italic>hull set<\/jats:italic>. The cardinality <jats:italic>h<\/jats:italic>(<jats:italic>G<\/jats:italic>) of a minimum hull set of <jats:italic>G<\/jats:italic> is the <jats:italic>hull number<\/jats:italic> of <jats:italic>G<\/jats:italic>. The <jats:italic>complementary prism<\/jats:italic> <jats:italic>GG\u0304<\/jats:italic> of a graph <jats:italic>G<\/jats:italic> arises from the disjoint union of the graph <jats:italic>G<\/jats:italic> and <jats:italic>G\u0304<\/jats:italic> by adding the edges of a perfect matching between the corresponding vertices of <jats:italic>G<\/jats:italic> and <jats:italic>G\u0304<\/jats:italic>. A graph <jats:italic>G<\/jats:italic> is <jats:italic>autoconnected<\/jats:italic> if both <jats:italic>G<\/jats:italic> and <jats:italic>G\u0304<\/jats:italic> are connected. Motivated by previous work, we study the hull number for complementary prisms of autoconnected graphs. When <jats:italic>G<\/jats:italic> is a split graph, we present lower and upper bounds showing that the hull number is unlimited. In the other case, when <jats:italic>G<\/jats:italic> is a non-split graph, it is limited by 3.<\/jats:p>","DOI":"10.1051\/ro\/2020089","type":"journal-article","created":{"date-parts":[[2020,8,25]],"date-time":"2020-08-25T19:44:08Z","timestamp":1598384648000},"page":"S2403-S2415","source":"Crossref","is-referenced-by-count":4,"special_numbering":"Supplement","title":["On the geodetic hull number for complementary prisms II"],"prefix":"10.1051","volume":"55","author":[{"given":"Diane","family":"Castonguay","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Erika M. 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