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Interlaced trees: A class of graceful trees

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Combinatorial Mathematics VI

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 748))

Abstract

Ringel conjectured that every tree has a graceful valuation. While this conjecture remains unsettled, it is apparent, from examples, that some trees have graceful valuations with additional properties which allow larger trees with graceful valuations to be constructed from them. We investigate here one such class of graceful trees.

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References

  1. I. Cahit, ‘Are all complete binary trees graceful?', Amer. Math. Monthly, 83 (1976), 35–37.

    Article  MathSciNet  MATH  Google Scholar 

  2. C.C. Chen, ‘On the enumeration of certain graceful graphs', in Proceedings of the International Conference on Combinatorial Theory, Canberra, 1977 (to appear).

    Google Scholar 

  3. C.C. Chen and P.Y. Lee, ‘Some problems in graph theory', SEA Bull. Math., 1 (1977), 38–43; 2 (1978), 39–41.

    MATH  Google Scholar 

  4. S.W. Golomb, ‘How to number a graph', in Graph Theory and Computing, ed. R.C. Read, (Academic Press, New York, 1972).

    Google Scholar 

  5. R.K. Guy, ‘Monthly research problems', Amer. Math. Monthly, 84 (1977), 807–815.

    Article  MathSciNet  MATH  Google Scholar 

  6. K.M. Koh, P.Y. Lee and T. Tan, ‘Fibonacci trees', SEA Bull. Math., 2 (1978), 45–47.

    MathSciNet  MATH  Google Scholar 

  7. K.M. Koh, D.G. Rogers and T. Tan, ‘On graceful trees', Nanta Mathematica, 10 (1977), 207–211.

    MathSciNet  MATH  Google Scholar 

  8. K.M. Koh and T. Tan, ‘Two theorems on graceful trees', Discrete Math., (to appear).

    Google Scholar 

  9. K.M. Koh and T. Tan, ‘A note on graceful trees', in Proceedings of the Third Southeast Asian Mathematical Symposium, Universiti Kebangsaan, Malaysia, 1978, (to appear).

    Google Scholar 

  10. D.G. Rogers, ‘A graceful algorithm', SEA Bull. Math., 2 (1978), 42–44.

    MathSciNet  MATH  Google Scholar 

  11. A. Rosa, ‘On certain valuations of the vertices of a graph', in Theory of Graphs, Proceedings of the International Symposium, Rome, 1966, (Gordon and Breach, New York, 1967).

    Google Scholar 

  12. R.G. Stanton and C.R. Zarnke, ‘Labellings of balanced trees', in Proceedings of the Fourth South Eastern Conference on Combinatorics, Graph Theory and Computing, Boca Raton 1973, Congressus Numerantium 8, (Utilitas Mathematica, Winnipeg, 1973).

    MATH  Google Scholar 

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A. F. Horadam W. D. Wallis

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© 1979 Springer-Verlag

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Koh, K.M., Tan, T., Rogers, D.G. (1979). Interlaced trees: A class of graceful trees. In: Horadam, A.F., Wallis, W.D. (eds) Combinatorial Mathematics VI. Lecture Notes in Mathematics, vol 748. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0102685

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  • DOI: https://doi.org/10.1007/BFb0102685

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09555-2

  • Online ISBN: 978-3-540-34857-3

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