Variety of mutual-visibility problems in hypercubesKorže, Danilo (Avtor) Vesel, Aleksander (Avtor) mutual visibilityhypercubebinary codeLet G be a graph and M ⊆ V(G). Vertices x, y ∈ M are M-visible if there exists a shortest x, y-path of G that does not pass through any vertex of M ⧵ {x, y}. We say that M is a mutual-visibility set if each pair of vertices of M is M-visible, while the size of any largest mutual-visibility set of G is the mutual-visibility number of G. If some additional combinations for pairs of vertices x, y are required to be M-visible, we obtain the total (every x, y ∈ V (G) are M-visible), the outer (every x ∈ M and every y ∈ V (G) ⧵ M are M-visible), and the dual (every x, y ∈ V (G) ⧵ M are M-visible) mutual-visibility set of G. The cardinalities of the largest of the above defined sets are known as the total, the outer, and the dual mutual-visibility number of G, respectively. We present results on the variety of mutual-visibility problems in hypercubes.Elsevier20252025-02-04 13:46:14Članek v reviji91779sl© 2024 The Author(s).