Variety of mutual-visibility problems in hypercubes

Let 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 , 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.