On the edge reconstruction of locally finite disconnected graphs with a finite number of components
type: Item
instance of: scholarly article
title: On the edge reconstruction of locally finite disconnected graphs with a finite number of components
zbMATH Open document ID: 0585.05024
DOI: 10.1007/BF02941501
author: Thomas Andreae
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 1985-01-01T00:00:00Z
review text: For a finite graph G on at least four vertices, G is edge-reconstructible if it has at least two nontrivial components. Here the author considers generalizations of this result to infinite disconnected graphs. He explains that dropping finite from the above statement probably leads to a difficult problem due to the existence of what he calls stable graphs; C is stable if \(E(C)=\emptyset\) and if, for each edge \(e\in E(C)\), there is a component B of C-e with \(B\simeq G\). He shows that if G is a locally finite graph with a finite number of components, then G is edge- reconstructible if it has at least two components that are neither trivial nor stable. He also edge-reconstructs a couple of more classes of locally finite graphs with a finite number of components.
reviewed by: R. L. Hemminger
Mathematics Subject Classification ID: 05C60
zbMATH DE Number: 3937209
zbMATH Keywords: edge-reconstruction
zbMATH Keywords: infinite graphs
zbMATH Keywords: infinite disconnected graphs
zbMATH Keywords: locally finite graph
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3937209