On the reconstruction of rayless infinite forests
Thomas Andreae, Rüdiger Schmidt · Journal of Graph Theory · 1984
Abstract A graph G is called strongly p‐reconstructible if it is (up to isomorphism) uniquely determined by the collection of its pairwise nonisomorphic subgraphs G – v where v is a pendent vertex of G. Using previous results of the second author concerning the structure of infinite rayless graphs it is shown that every rayless forest with an infinite edge‐set is strongly p‐reconstructible. This result is applied to the classical reconstruction problem to find that every infinite rayless forest G with a finite number of components is reconstructible; i.e., G is (up to isomorphism) uniquely determined by its collection of vertex‐deleted subgraphs. Furthermore, an example is given which shows that nonreconstructible rayless forests with a countable number of components exist.