论文标题
在$ p_3 $ - 赫尔号和广义彼得森图的感染时间
On the $P_3$-hull number and infecting times of generalized Petersen graphs
论文作者
论文摘要
$ p_3 $ - 图的图是一组感染顶点的最小基数，最终将在规则下最终感染整个图形，如果未感染两个或多个邻居感染了未感染的节点。在本文中，我们研究了$ p_3 $ hull的通用彼得森图和许多密切相关的图表，这些图是由手术或更广泛的排列引起的。此外，针对广义彼得森图计算了一组最小基数的补充组件的数量，并显示为始终为$ 1 $或$ 2 $。此外，研究了感染最小基数的感染时间。提供界限，并在特殊情况下提供完整的信息。
The $P_3$-hull number of a graph is the minimum cardinality of an infecting set of vertices that will eventually infect the entire graph under the rule that uninfected nodes become infected if two or more neighbors are infected. In this paper, we study the $P_3$-hull number for generalized Petersen graphs and a number of closely related graphs that arise from surgery or more generalized permutations. In addition, the number of components of the complement of an infecting set of minimum cardinality is calculated for the generalized Petersen graph and shown to always be $1$ or $2$. Moreover, infecting times for infecting sets of minimum cardinality are studied. Bounds are provided and complete information is given in special cases.
