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Stable trees

Published online by Cambridge University Press:  09 April 2009

D. A. Holton
D. A. Holton
Affiliation:
University of MelbourneParkville, 3052, Australia
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Abstract: We show that a tree is stable if and only if its automorphism group contains a transposition. The method is constructive and so enables a stabilising sequence to be found.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 15 , Issue 4 , June 1973 , pp. 476 - 481
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Harary, F., Graph Theory (Addison Wesley, 1969).CrossRefGoogle Scholar
[2]Heffernan, P., ‘Trees’, Masters Thesis, University of Christchurch, N. Z., 1972.Google Scholar
[3]Holton, D. A., ‘A report on stable graphs’ J. Aust. Math., 4, (1973) 151–158.Google Scholar
[4]Holton, D. A., ‘Two applications of semi-stability’ Discrete Maths., 15, (1973) 163–171.Google Scholar
[5]Wielandt, H., Finite Permutation Groups (Academic Press, 1964).Google Scholar