Burning Numbers of Path forests and Spiders

Abstract

Graph burning is a deterministic discrete-time graph process that can be interpreted as a model for the spread of influence in social networks. The burning number of a graph G is the minimum number of steps in a graph burning process for G. It is shown that the graph burning problem is NP-complete even for trees and path forests. In this paper, we first determine the burning numbers of path forests with at most three components and then use these results to determine the burning numbers of all spiders with three arms.