On the diameter of the rotation graph of binary coupling trees

Authors:
V. Fack;S. Lievens;J. Van der Jeugt
Affiliations:
Department of Applied Mathematics and Computer Science, University of Ghent, Krijgslaan 281-S9, B-9000 Gent, Belgium;Department of Applied Mathematics and Computer Science, University of Ghent, Krijgslaan 281-S9, B-9000 Gent, Belgium;Department of Applied Mathematics and Computer Science, University of Ghent, Krijgslaan 281-S9, B-9000 Gent, Belgium
Venue:
Discrete Mathematics
Year:
2002

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Abstract

A binary coupling tree on n + 1 leaves is a binary tree in which the leaves have distinct labels. 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 of Gn for values up to 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 of Gn grows like nlg(n).