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On the power of a perturbation for testing non-isomorphism of graphs

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Abstract

In this paper we prove an inverted version of A. J. Schwenk's result, which in turn is related to Ulam's reconstruction conjecture. Instead of deleting vertices from an undirected graphG, we add a new vertexv and join it to all other vertices ofG to get a perturbed graphG+v. We derive an expression for the characteristic polynomial of the perturbed graphG+v in terms of the characteristic polynomial of the original graphG. We then show the extent to which the characteristic polynomials of the perturbed graphs can be used in determining whether two graphs are non-isomorphic.

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References

  1. L. Collatz and U. Sinogowitz,Spektren endlichen Graphen, Abh. Math. Sem. Univ. Hamburg 21 (1957), 63–77.

    Google Scholar 

  2. M. Behzad, G. Chartrand and L. Lesniak-Foster,Graphs and Digraphs, Prindle, Weber & Schmidt, Boston, MA, 1979.

    Google Scholar 

  3. J. A. Bondy and R. L. Hemminger,Graph reconstruction — a survey, J. Graph Theory 1 (1977), 227–268.

    Google Scholar 

  4. N. Deo,Graph Theory with Applications to Engineering and Computer Science, Prentice-Hall, Englewood Cliffs, NJ, 1974.

    Google Scholar 

  5. F. Harary,Graph Theory, Addison-Wesley, Reading, Mass., 1969.

    Google Scholar 

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

    Google Scholar 

  7. P. J. Kelly,A Congruence theorem for trees, Pacific J. Math. 7 (1957), 961–968.

    Google Scholar 

  8. C. St. J. A. Nash-Williams,The reconstruction problem, inSelected Topics in Graph Theory, L. W. Beineke and R. J. Wilson Eds., Academic Press, NY, 1978.

    Google Scholar 

  9. A. J. Schwenk,Spectral reconstruction problems, inTopics in Graph Theory, F. Harary Ed., Annals of the New York Academy of Sciences 328, 1979, 183–189.

  10. S. M. Ulam,A Collection of Mathematical Problems, Wiley (Interscience), NY, 1960.

    Google Scholar 

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Authors and Affiliations

  1. Computer Science Department, Iowa State University, 50011, Ames, Iowa, USA

    G. M. Prabhu & Narsingh Deo

  2. Computer Science Department, Washington State University, 99164-1210, Pullman, Washington, USA

    G. M. Prabhu & Narsingh Deo

Authors
  1. G. M. Prabhu
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  2. Narsingh Deo
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Additional information

This work was supported by the U.S. Army Research Office under Grant DAAG29-82-K-0107.

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Prabhu, G.M., Deo, N. On the power of a perturbation for testing non-isomorphism of graphs. BIT 24, 302–307 (1984). https://doi.org/10.1007/BF02136028

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  • DOI: https://doi.org/10.1007/BF02136028

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