Skip to main content
SpringerLink
Log in

Computing the characteristic polynomial of a tree

Berechnung des charakteristischen Polynoms eines Baumes

  • Published:
Computing Aims and scope Submit manuscript

Abstract

We present an O(n 3)-algorithm for computing the characteristic polynomial of a tree in a certain factorized form. Each factor is caused by some structural property of the tree.

Zusammenfassung

Wir stellen einen O(n 3)-Algorithmus zur Berechnung des charakteristischen Polynoms eines Baumes vor. Der Algorithmus liefert dieses Polynom in einer faktorisierten Form, wobei jeder Faktor durch eine gewisse Struktureigenschaft des Baumes bestimmt ist.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Collatz, L., Singowitz, U.: Spektren unendlicher Graphen. Abh. Math. Sem. Univ. Hamburg21 63–77 (1957).

    Google Scholar 

  2. Cvetkovic, D. M., Doob, M., Sachs, H.: Spectra of Graphs. New York: Academic Press 1980.

    Google Scholar 

  3. Gutman, I.: Generalizations of a recurrence relation for the characteristic polynomials of trees. Publ. Inst. Math. (Beograd)21 (35), 75–80 (1977).

    Google Scholar 

  4. Harary, F., King, C., Mowshowitz, A., Read R. C.: Cospectral graphs and digraphs. Bull. London Math. Soc.3, 321–328 (1971).

    Google Scholar 

  5. Lihtenbaum, L. M.: Charakteristische Zahlen ungerichteter Graphen (Russ.) In: Publ. Math. Congress of USSR1, 135 (1956).

  6. Lovasz, L., Pelikan, J.: On the eigenvalues of trees. Periodica Math. Hung.3, (1–2), 175–182 (1973).

    Article  Google Scholar 

  7. Mowshowitz, A.: The characteristic polynomial of a graph. J. Comb. Theory12(b), 177–193 (1972).

    Article  Google Scholar 

  8. Rempel, J., Schwolow, K. H.: Ein Verfahren zur Faktorisierung des charakteristischen Polynoms eines Graphen. Wiss. Z. TH Ilmenau23, 25–39 (1977).

    Google Scholar 

  9. Sachs, H.: Über Teiler, Faktoren und charakteristische Polynome von Graphen I. Wiss. Z. TH Ilmenau12, 7–12 (1966).

    Google Scholar 

  10. Sachs, H.: Über Teiler, Faktoren und charakteristische Polynome von Graphen II. Wiss. Z. TH Ilmenau13, 405–412 (1967).

    Google Scholar 

  11. Schwenk, A. J.: Computing the characteristic polynomial of a graph. In: Graphs and Combinatorics (Lecture Notes in Math 406, R. Bari and F. Harary, eds.), pp. 153–172. Berlin-Heidelberg-New York: Springer 1974.

    Google Scholar 

  12. Tinhofer, G., Schreck, H.: Linear time tree codes. Computing33, 211–225 (1984).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematisches Institut, Technische Universität München, Barer Strasse 23, Postfach 202420, D-8000, München 2, Federal Republic of Germany

    G. Tinhofer & H. Schreck

Authors
  1. G. Tinhofer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Schreck
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Dedicated to Professor R. Albrecht on the occasion of his 60th birthday

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tinhofer, G., Schreck, H. Computing the characteristic polynomial of a tree. Computing 35, 113–125 (1985). https://doi.org/10.1007/BF02260499

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02260499

AMS Subject Classifications

Key words

Search

Navigation