On the $P_3$-hull number and infecting times of generalized Petersen graphs

Abstract

The P 3 -hull number of a graph is the size of a minimal 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 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 a minimal infecting set is calculated for the Petersen graph and shown to always be 1 or 2. In addition, infecting times for a minimal infecting set are studied. Bounds are given and complete information is given in special cases.