Abstract
We prove that the degree sequence of an infinite graph is reconstructible from its family of vertex-deleted subgraphs. Furthermore, as another result concerning the reconstruction of infinite graphs, we prove that the number c( G) of components of an infinite graph G is reconstructible if there is at least one vertex x in G with the following property: If x is deleted from G, then the component of G containing x splits into a finite number of components. In particular, this implies that c( G) is reconstructible if there is at least one vertex of finite degree in G.
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