%0 Generic %1 herden2021p3hull %A Herden, Daniel %A Meddaugh, Jonathan %A Sepanski, Mark %A Echols, Isaac %A Garcia-Montoya, Nina %A Hammon, Cordell %A Huang, Guanjie %A Kraus, Adam %A Menendez, Jorge Marchena %A Mohn, Jasmin %A Jiménez, Rafael Morales %D 2021 %K diffusion infection_graphs thesis_topic %T On the $P_3$-hull number and infecting times of generalized Petersen graphs %U http://arxiv.org/abs/2201.00078 %X 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.

@misc{herden2021p3hull, 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.}, added-at = {2022-01-04T14:12:04.000+0100}, author = {Herden, Daniel and Meddaugh, Jonathan and Sepanski, Mark and Echols, Isaac and Garcia-Montoya, Nina and Hammon, Cordell and Huang, Guanjie and Kraus, Adam and Menendez, Jorge Marchena and Mohn, Jasmin and Jiménez, Rafael Morales}, biburl = {https://www.bibsonomy.org/bibtex/2aab88326a458ab62223fe9a02abe67d7/j.c.m.janssen}, description = {On the $P_3$-hull number and infecting times of generalized Petersen graphs}, interhash = {75311d2b3017ee79bea28f4b629724e1}, intrahash = {aab88326a458ab62223fe9a02abe67d7}, keywords = {diffusion infection_graphs thesis_topic}, note = {cite arxiv:2201.00078Comment: 8 pages}, timestamp = {2022-01-04T14:12:04.000+0100}, title = {On the $P_3$-hull number and infecting times of generalized Petersen graphs}, url = {http://arxiv.org/abs/2201.00078}, year = 2021 }