Let $G=(V,E)$ be a graph and $P\subseteq V$ a set of points. Two points are mutually visible if there is a shortest path between them without further points. $P$ is a mutual-visibility set if its points are pairwise mutually visible. The mutual-visibility number of $G$ is the size of any largest mutual-visibility set. In this paper we start the study about this new invariant and the mutual-visibility sets in undirected graphs. We introduce the mutual-visibility problem which asks to find a mutual-visibility set with a size larger than a given number. We show that this problem is NP-complete, whereas, to check whether a given set of points is a mutual-visibility set is solvable in polynomial time. Then we study mutual-visibility sets and mutual-visibility numbers on special classes of graphs, such as block graphs, trees, grids, tori, complete bipartite graphs, cographs. We also provide some relations of the mutual-visibility number of a graph with other invariants.

翻译：让 $G = (V, E) $ 是一个图表, $P\ subseteq V 一组点数。 如果两个点之间有一个最短的路径, 没有进一步的点数, 两点是互相可见的。 $P 是一个共同可见的集合。 如果给定的点是双向的, 则其相互可见的集合值为任何最大的共同可见集的大小 。 在本文中, 我们开始在未定向的图表中研究这个新的变量和相互可见集。 我们引入了相互可见的问题, 需要找到一个比给定数大得多的相见集。 我们显示, 这个问题是完整的 NP, 而要检查给定的一组点数是否在多元时间内是相互可见的。 然后我们研究特殊图表类别, 如块图、 树、 网格、 托里、 完整的双向图形、 cograph 上的相互可见集数。 我们还提供一个图表相互可见数的某种关系。