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Another class of graceful trees

Part of: Graph theory

Published online by Cambridge University Press:  09 April 2009

K. M. Koh ,
D. G. Rogers  and
T. Tan
K. M. Koh
Affiliation:
Department of Mathematics, National University of Singapore, Singapore, 1025
D. G. Rogers
Affiliation:
Department of Mathematics, University of Kansas, Lawrence, Kansas 66045, U.S.A.
T. Tan
Affiliation:
Department of Mathematics, University of Kansas, Lawrence, Kansas 66045, U.S.A.
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Abstract

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We discuss the problem of constructing large graceful trees from smaller ones and provide a partial answer in the case of the product tree Sm {g} by way of a sample of sufficient conditions on g. Interlaced trees play an important role as building blocks in our constructions, although the resulting valuations are not always interlaced.

MSC classification

Secondary: 05C05: Trees
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 31 , Issue 2 , August 1981 , pp. 226 - 235
Copyright
Copyright © Australian Mathematical Society 1982

References

Bermond, J. C. (1979), ‘Graceful graphs, radio antennae and French windmills, in combinatorics and graph theory’, Research Notes in Mathematics 34, ed. Wilson, R. J., pp. 18–37 (Pitman, London).Google Scholar
Cahit, I. (1976), ‘Are all complete binary trees graceful?’ Amer. Math. Monthly 83, 35–36.Google Scholar
Golomb, S. W. (1972), ‘How to number a graph’, in Graph theory and computing, ed. Read, R. C., pp. 23–27 (Academic Press, New York).CrossRefGoogle Scholar
Guy, R. K. (1977), Monthly research problems, Amer. Math. Monthly 84, 807–815.Google Scholar
Koh, K. M., Rogers, D. G. and Tan, T. (1979), ‘Interlaced trees: a class of graceful trees’ Combinatorical mathematics VI: Proceedings of Sixth Australian Conference on Combinatorial Mathematics, Armidale, 1978, ed. Horadam, A. and Wallis, W. D., pp. 65–78 (Lecture Notes in Mathematics 748, Springer Verlag, Berlin).CrossRefGoogle Scholar
Pastel, A. M. and Raynaud, H. (1978), Les oliviers soft gracieux, (Publications Université de Grenoble).Google Scholar
Rosa, A. (1967), ‘On certain valuations of the vertices of a graph’, Theory of graphs, Proceedings of International Symposium, Rome 1966 ed. Rosenstiehl, P., pp. 349–355 (Gordon and Breach, New York).Google Scholar
Rogers, D. G. (1978), ‘A graceful algorithm’, Southeast Asian Bull. Math. 2, 42–44.Google Scholar
Cornejo, S. Ruiz (1979), ‘Another class of graceful trees’, Research Report, University of Valparaiso, Chile.Google Scholar
Stanton, R. G. and Zarnke, C. R. (1973), ‘Labellings of balanced trees’, Proceedings of the Fourth South-Eastern Conference on Combinatorics, Graph Theory and Computing, Boca Raton, 1973, Congressus Numerantium VIII, pp. 479–495 (Utilitas Mathematica, Winnipeg).Google Scholar