@article{Sim2024, 
author = {Kai An Sim and Kok Bin Wong},
title = {On the cooling number of the generalized Petersen graphs},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {12},
pages = {36351-36370},
keywords = {cooling number, generalized Petersen graphs},
url = {https://www.sciopen.com/article/10.3934/math.20241724},
doi = {10.3934/math.20241724},
abstract = {Recently, Bonato et al. (2024) introduced a new graph parameter, which is the cooling number of a graph  G, denoted as CL (G). In contrast with burning which seeks to minimize the number of rounds to burn all vertices in a graph, cooling seeks to maximize the number of rounds to cool all vertices in the graph. Cooling number is the compelling counterpart to the well-studied burning number, offering a new perspective on dynamic processes within graphs. In this paper, we showed that the cooling number of a classic cubic graph, the generalized Petersen graphs  P(n,k), is  ⌊n2k⌋+⌊k+12⌋+O(1) by the use of vertex-transitivity and combinatorial arguments. Particularly, we determined the exact values for CL (P(n,1)) and CL (P(n,2)).}
}