论文标题
通过总相互可视性在强产物中相互可视性
Mutual-visibility in strong products of graphs via total mutual-visibility
论文作者
论文摘要
令$ g $为图形，$ x \ subseteq v（g）$。然后，如果$ x $的每对顶点是由$ x $连接的，则$ x $是一个相互可视性的集合，而$ x $中没有内部顶点的地理位置连接。 $ g $的相互可见性数量$μ（g）$是最大的相互视野集的基础。在本文中，研究了强乘积图的相互可见性数量。作为此的工具，引入了总共相互可视性集。一路上，介绍了此类集合的基本属性。强产物的（总）相互可见性数量以两种方式从下面界定，并完全决定了强大的任意维度网格。分别研究了强大的棱镜，并给出了几个紧密的界限，以使其相互可见的数字。
Let $G$ be a graph and $X\subseteq V(G)$. Then $X$ is a mutual-visibility set if each pair of vertices from $X$ is connected by a geodesic with no internal vertex in $X$. The mutual-visibility number $μ(G)$ of $G$ is the cardinality of a largest mutual-visibility set. In this paper, the mutual-visibility number of strong product graphs is investigated. As a tool for this, total mutual-visibility sets are introduced. Along the way, basic properties of such sets are presented. The (total) mutual-visibility number of strong products is bounded from below in two ways, and determined exactly for strong grids of arbitrary dimension. Strong prisms are studied separately and a couple of tight bounds for their mutual-visibility number are given.
