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∖{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.

中文翻译：

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超立方体中的各种互能性问题


设 G 为图形，M⊆V（G）。如果存在 G 的最短 x，y 路径，且该路径不穿过 M∖{x，y}，则顶点 x，y∈M 是 M 可见的。如果 M 的每对顶点都是 M 可见的，则我们说 M 是互能可见集，而 G 的任何最大互能可见集的大小是 G 的互能可见数。如果需要顶点对 x，y 的一些附加组合是 M 可见的，我们得到 G 的总（每个 x，y∈V（G） 都是 M 可见的）、外部（每个 x∈M 和每个 y∈V（G）∖M 都是 M 可见的）和对偶（每个 x，y∈V（G）∖M 都是 M 可见的）G 的互能可见集。上述定义集中最大的基数分别称为 G 的总数、外部和双重互能数。