Abstract

A binary coupling tree on n+1 leaves is a 0--2-tree in which each leaf has a distinct label. The rotation graph Gn is defined as the graph of all binary coupling trees on n + 1 leaves, with edges connecting trees that can be transformed into each other by a single rotation. In this paper we study distance properties of the graph Gn . Exact results for the diameter d(Gn ) for values upto n = 10 are obtained. For larger values of n we prove upper and lower bounds for the diameter, which yield the result that the diameter d(Gn ) grows like n lg(n). Corresponding author : V. Fack, Department of Applied Mathematics and Computer Science, University of Ghent, Krijgslaan 281-S9, B-9000 Gent, Belgium. Tel. ++ 32 9 2644808; Fax ++ 32 9 2644995; E-mail Veerle.Fack@rug.ac.be. 1 Research Associate of the Fund for Scientific Research -- Flanders (Belgium) 1 Introduction Binary coupling trees arise in the context of the quantum theory of angular momentum, where they represent coupling schemes in...