Volume 55, 2021Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|Page(s)||S2403 - S2415|
|Published online||02 March 2021|
On the geodetic hull number for complementary prisms II
INF, Universidade Federal de Goiás, Goiânia, Brazil
Accepted: 20 August 2020
In the geodetic convexity, a set of vertices S of a graph G is convex if all vertices belonging to any shortest path between two vertices of S lie in S. The convex hull H(S) of S is the smallest convex set containing S. If H(S) = V (G), then S is a hull set. The cardinality h(G) of a minimum hull set of G is the hull number of G. The complementary prism GḠ of a graph G arises from the disjoint union of the graph G and Ḡ by adding the edges of a perfect matching between the corresponding vertices of G and Ḡ. A graph G is autoconnected if both G and Ḡ are connected. Motivated by previous work, we study the hull number for complementary prisms of autoconnected graphs. When G is a split graph, we present lower and upper bounds showing that the hull number is unlimited. In the other case, when G is a non-split graph, it is limited by 3.
Mathematics Subject Classification: 05C12 / 05C76
Key words: Geodetic convexity / hull set / hull number / complementary prism
© EDP Sciences, ROADEF, SMAI 2021
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