论文标题
遍历一般位置的图
Traversing a graph in general position
论文作者
论文摘要
令$ g $为图。假设对一组顶点的每个顶点$ s \ subseteq v（g）$分配了机器人。在每个阶段，一个机器人可以移至相邻的顶点。然后，$ s $是$ g $的移动通用位置集，如果存在一系列机器人的动作，以便始终访问$ g $的所有顶点，同时始终保持一般位置属性。 $ g $的移动通用位置是$ g $的最大移动通用位置集的基础。在本文中，给出了移动通用位置编号的界限，并确定了某些常见类图的精确值，包括块图，扎根产品，独一图形，笛卡尔产品，图形连接，旋转图$ k（n，2）$和线图。
Let $G$ be a graph. Assume that to each vertex of a set of vertices $S\subseteq V(G)$ a robot is assigned. At each stage one robot can move to a neighbouring vertex. Then $S$ is a mobile general position set of $G$ if there exists a sequence of moves of the robots such that all the vertices of $G$ are visited whilst maintaining the general position property at all times. The mobile general position number of $G$ is the cardinality of a largest mobile general position set of $G$. In this paper, bounds on the mobile general position number are given and exact values determined for certain common classes of graphs including block graphs, rooted products, unicyclic graphs, Cartesian products, joins of graphs, Kneser graphs $K(n,2)$, and line graphs of complete graphs.
