It is proved that decomposable graphs are set recognizable and that the index graph of the canonical decomposition as well as the graphs induced on the maximal autonomous sets of vertices are set reconstructible. From these results, we obtain set reconstructibility for many decomposable graphs as well as a concise description of the decomposable graphs for which set reconstruction remains an open problem.

中文翻译：

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设置对可分解图的识别和重构的步骤

证明了可分解图是集合可识别的，并且正则分解的索引图以及在最大自治顶点集上导出的图是集合可重构的。从这些结果中，我们获得了许多可分解图的集合可重构性，以及对集合重构仍然是一个悬而未决问题的可分解图的简明描述。