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Circulant matrices and the spectra of de Bruijn graphs

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Abstract

The block structure of k-circulant matrices A of order n (k≥2, k¦n) is investigated and statements, enabling to reduce a series of problems with the matrices A+AT to analogous problems with matrices of lower order, namely the blocks of the matrices A and AT, are proved. The spectrum and the number of spanning trees of an undirected de Bruijn graph are obtained.

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References

  1. V. V. Voevodin and E. E. Tyrtyshnikov, Numerical Processes with Teoplitz Matrices [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  2. C. M. Ablow and J. L. Brenner, “Roots and canonical forms for circulant matrices,” Trans. Amer. Math. Soc.,107, No. 2, 360–376 (1963).

    Google Scholar 

  3. N. G. de Bruijn, “A combinatorial problem,” Indag. Math.,8, No. 4, 461–467 (1946).

    Google Scholar 

  4. M. I. Kratko and V. V. Strok, “de Bruijn sequences with constraints,” in: Questions of Cybernetics. Combinatorial Analysis and Theory of Graphs [in Russian], Nauka, Moscow (1980), pp. 80–84.

    Google Scholar 

  5. D. M. Cvetković, M. Doob, and H. Sachs, Spectra of Graphs-Theory and Applications, Academic Press, New York (1980).

    Google Scholar 

  6. W. B. Jones and W. J. Thron, Continued Fractions, Addison-Wesley, Reading, Mass. (1980).

    Google Scholar 

  7. J. Riordan, Combinatorial Identities, Wiley, New York (1968).

    Google Scholar 

  8. I. Gutman, “Characteristic and matching polynomials of some compound graphs,” Publ. Inst. Math. (Beograd),27, 61–66 (1980).

    Google Scholar 

  9. Gh. RĂut, “Spectra of complete k-ary trees,” Stud. Cerc. Mat.,35, No. 3, 183–188 (1983).

    Google Scholar 

  10. N. P. Khomenko and V. V. Strok, “T-factorization ofGB-graphs,” in: Graph Theory [in Russian], Inst. Mat., Akad. Nauk UkrSSR, Kiev (1977).

    Google Scholar 

  11. V. Strok and E. Yaworski, “Spectrum of the binary de Bruijn graph,” in: Seventeenth Yugoslav Symp. Oper. Res. (Dubrovnik-Kupari, October 9–12, 1990), Naucna Knjiga, Beograd (1990), pp. 165–168.

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Academy of Sciences of Ukraine, Kiev

    V. V. Strok

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  1. V. V. Strok
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 11, pp. 1571–1579, November, 1992.

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Strok, V.V. Circulant matrices and the spectra of de Bruijn graphs. Ukr Math J 44, 1446–1454 (1992). https://doi.org/10.1007/BF01071520

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  • DOI: https://doi.org/10.1007/BF01071520

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