广义Petersen图的$P_3$ -壳数和感染次数
On the $P_3$-hull number and infecting times of generalized Petersen graphs
摘要：
图的$P_3$ -壳数是在两个或多个邻居被感染的情况下，未感染节点被感染的规则下，最终将感染整个图的感染顶点集的最小基数。在本文中，我们研究了广义Petersen图和一些密切相关的图，手术或更广义的置换产生的$P_3$ -壳数。此外，还计算了广义Petersen图的最小基数传染集的补集的分量数，并证明了它总是$1$或$2$ .此外，还研究了最小基数感染集的感染时间。在特殊情况下提供边界和完整的信息。
英文摘要：
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.
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