The problem of graph burning was firstly introduced as a model for different processes of social and network interactions. Recently, the authors of the present paper developed methods of algebraic topology for investigation of this problem. This approach is based on the new definition of burning process which excludes the possibility to choose at any moment vertex for burning from the set of vertices which are already burned at this moment. In this paper we continue to study such burning process using algebraic topology methods. We prove the result about relations between burnings of a graph and burnings of its spanning trees that is similar to the classical case. Afterwards, we describe properties of trees burnings. In particular, we prove that a burning of a tree defines a structure of a digraph on the tree and investigate this structure. We introduce and study a strong burning configuration space of a graph and new strong burning homology which are similar to burning homology defined in our previous paper, but arise from burning homomorphism.

翻译：图燃烧问题最初是作为社交与网络交互中不同过程的模型被提出的。近期，本文作者发展了代数拓扑方法来研究该问题。此方法基于燃烧过程的新定义，该定义排除了在任意时刻从当前已燃烧顶点集合中选择顶点进行燃烧的可能性。本文中，我们继续使用代数拓扑方法研究此类燃烧过程。我们证明了关于图燃烧与其生成树燃烧之间关系的结果，该结果与经典情形相似。随后，我们描述了树燃烧的性质。特别地，我们证明了树的燃烧可在树上定义一个有向图结构，并研究了该结构。我们引入并研究了图的强燃烧构型空间及新的强燃烧同调，这些概念与我们先前论文中定义的燃烧同调相似，但源于燃烧同态。