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Recent results on trees

  • Part I: Invited Papers
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Graphs and Combinatorics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 406))

Abstract

Our object is to present six theorems on trees discovered since the appearance of the book [4]. These deal with (1) trees with hamiltonian square, (2) path numbers, (3) the tree graph of a graph, (4) the intersection graph of subtrees of a tree, (5) cospectral trees, and (6) the probability of an endpoint.

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References

  1. Buneman, P., A Characterization of Rigid Circuit Graphs, Discrete Math., to appear.

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  2. Collatz, L., and Sinogowitz, U., Spektren endlicher Graphen, Abh. Math. Sem. Univ. Hamburg 211 (1957) 64–77.

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  3. Fleishner, H. J., The Square of Every Nonseparable Graph is Hamiltonian, J. Combinatorial Theory, to appear.

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  4. Harary, F., Graph Theory, Addison-Wesley, Reading, 1969.

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  5. Harary, F., and Holzmann, C., On the Tree Graph of a Matroid, SIAM J. Appl. Math. 22 (1972) 187–193.

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  6. Harary, F., and Schwenk, A. J., Trees with Hamiltonian Square, Mathematika 18 (1971) 138–140.

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  7. Harary, F., and Schwenk, A. J., Evolution of the Path Number of a Graph. Graph Theory and Computing (R.C. Read, ed.) Academic Press, New York, 1972, 39–45.

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  10. Robinson, R. W., and Schwenk, A. J., The Probability of an Endpoint in a Large Random Tree, Proc. Camb. Phil. Soc., submitted.

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  11. Schwenk, A. J., Almost All Trees are Cospectral, New Directions in the Theory of Graphs (F. Harary, ed.) Academic Press, New York, 1973, 275–307.

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Authors and Affiliations

  1. University of Michigan, USA

    Frank Harary

Authors
  1. Frank Harary
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Editor information

Ruth A. Bari Frank Harary

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© 1974 Springer-Verlag Berlin

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Harary, F. (1974). Recent results on trees. In: Bari, R.A., Harary, F. (eds) Graphs and Combinatorics. Lecture Notes in Mathematics, vol 406. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066429

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  • DOI: https://doi.org/10.1007/BFb0066429

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06854-9

  • Online ISBN: 978-3-540-37809-9

  • eBook Packages: Springer Book Archive

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