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

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

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.

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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.

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  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.

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  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.

    CrossRef  MATH  Google Scholar 

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

    CrossRef  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.

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

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

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  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.

    CrossRef  Google Scholar 

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

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© 1981 Springer-Verlag

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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

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

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11151-1

  • Online ISBN: 978-3-540-47037-3

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