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Reconstructing the degree sequence and the number of components of an infinite graph

✍ Scribed by Thomas Andreae

Publisher: Elsevier Science
Year: 1982
Tongue: English
Weight: 812 KB
Volume: 39
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(82)90035-8

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✦ Synopsis

We prove that the degree sequence of an infinite graph is reconstructibjle 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 re~ons~uct~b~e if there is at Ieast one vertex x in G with the following property: If x is deleted from 6, 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 csf finite degree in G.

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