Reconstruction of infinite locally finite connected graphs (Q1406548)

The authors continue previous work of Bondy and Hemminger, Thomassen, Andreae, and Nash-Williams on the reconstruction of infinite locally finite connected graphs; see \textit{C. St. J. A. Nash-Williams} [Discrete Math. 95, 221-229 (1991; Zbl 0759.05066)] for a survey. The authors' investigations are based on the concept of order of an end which was introduced by \textit{H. A. Jung} [Math. Nachr. 41, 1-22 (1969; Zbl 0177.27001)]. The main result is that a locally finite connected graph is reconstructible if it contains no end-respecting subdivision of the dyadic tree and if it has at least two ends of maximal order.