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 b ( G ) of a graph G is the minimum number of steps in a graph burning process for G . Bonato et al. (2014) conjectured that b ( G ) ≤ ⌈ n ⌉ for any connected graph G of order n . In this paper, we confirm this conjecture for caterpillars. We also determine the burning numbers of caterpillars with at most two stems and a subclass of the class of caterpillars all of whose spine vertices are stems.

中文翻译：

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燃烧的毛毛虫数

摘要 图燃烧是一种确定性离散时间图过程，可以解释为社交网络中影响力传播的模型。图 G 的燃烧次数 b ( G ) 是 G 的图燃烧过程中的最小步骤数。博纳托等人。(2014) 推测 b ( G ) ≤ ⌈ n ⌉ 对于任何 n 阶连通图 G。在本文中，我们证实了毛毛虫的这一猜想。我们还确定了最多具有两个茎和所有脊椎顶点都是茎的毛虫类的子类的毛虫的燃烧数量。