Skip to main content

A graph theoretical recurrence formula for computing the characteristic polynomial of a matrix

  • Contributed Papers
  • Conference paper
  • First Online:
Combinatorics and Graph Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 885))

  • 1142 Accesses

Abstract

In this paper, a recurrence formula for computing the characteristic polynomial of a graph due to A.J. Schwenk is generalised to arbitrary networks, and some useful reductions of this formula are cited.

The work was done when the author was at Mehta Research Institute, Allahabad.

Research supported by the Council of Scientific and Industrial Research, New Delhi, and partially by Government of India Research Project No. HCS/DST/409/76.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. B.D. Acharya, A graph theoretical expression for the characteristic polynomial of a matrix, Proc. Nat. Acad. Sci. (India), 49 (Sec. A) (1979).

    Google Scholar 

  2. W.K. Chen, Applied Graph Theory: Graphs and Electrical Networks, North-Holland, Amsterdam, 1975.

    Google Scholar 

  3. M.K. Gill and B.D. Acharya, A recurrence formula for computing the characteristic polynomial of a sigraph, J. Comb. Infor. Sys. Sci., 5(1) (1980), 1–5.

    MathSciNet  MATH  Google Scholar 

  4. F. Harary, A graph theoretical method for complete reduction of a matrix with a view toward finding its eigenvalues, J. Math. Physics, 38(1959), 104–111.

    Article  MATH  Google Scholar 

  5. F. Harary, The determinant of the adjacency matrix of a graph, SIAM Rev., 4(3) (1962), 202–210.

    Article  MathSciNet  MATH  Google Scholar 

  6. F. Harary, R. Z. Norman, and D. Cartwright, Structural models: An introduction to the theory of directed graphs, Wiley, 1965.

    Google Scholar 

  7. F. Harary, Graph Theory, Addison-Wesley, Reading, Mass., 1972.

    MATH  Google Scholar 

  8. D. König, Theorie der endlichen und unendlichen graphen, Leipzig, 1936 (Reprinted New York, 1950).

    Google Scholar 

  9. M.J. Rigby, R.B. Mallion, and A.C. Day, Comment on a graph theoretical description of heteroconjugated molecules, Chemical Physics Letters, 51(1) (1977), 178–182.

    Article  Google Scholar 

  10. A.J. Schwenk, Computing the characteristic polynomial of a graph, Springer-Verlag Lecture Notes in Mathematics, Vol. 406 (1974), 153–172.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Siddani Bhaskara Rao

Rights and permissions

Reprints and permissions

Copyright information

© 1981 Springer-Verlag

About this paper

Cite this paper

Gill, M.K. (1981). A graph theoretical recurrence formula for computing the characteristic polynomial of a matrix. In: Rao, S.B. (eds) Combinatorics and Graph Theory. Lecture Notes in Mathematics, vol 885. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092268

Download citation

  • DOI: https://doi.org/10.1007/BFb0092268

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11151-1

  • Online ISBN: 978-3-540-47037-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics