On the edge reconstruction of locally finite disconnected graphs with a finite number of components
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.
scientific article; zbMATH DE number 3937209
scientific article