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There Is No Strongly Regular Graph with Parameters (460, 153, 32, 60)

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Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan

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Abstract

We prove that there is no strongly regular graph (SRG) with parameters (460, 153, 32, 60). The proof is based on a recent lower bound on the number of 4-cliques in a SRG and some applications of Euclidean representation of SRGs.

Dedicated to Ian H. Sloan on the occasion of his 80th birthday.

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References

  1. Bondarenko, A., Prymak, A., Radchenko, D.: Non-existence of (76, 30, 8, 14) strongly regular graph and some structural tools. Linear Algebra Appl. 527, 53–72 (2017)

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  2. Bondarenko, A., Prymak, A., Radchenko, D.: Supplementary files for the proof of non-existence of SRG(76,30,8,14). Preprint available at http://prymak.net/SRG-76-30-8-14/

  3. Brouwer, A. E.: Parameters of strongly regular graphs, Electronically published tables. http://www.win.tue.nl/~aeb/graphs/srg/srgtab.html

  4. Brouwer, A.E., Haemers, W.H.: Spectra of Graphs. Universitext. Springer, Berlin (2012)

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  5. Brouwer, A.E, van Lint, J.H.: Strongly regular graphs and partial geometries. In: Proceedings of the Conference Enumeration and Design, Waterloo, ON, 1982, pp. 85–122, Academic, Toronto, ON (1984)

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  6. Cameron, P. J.: Strongly Regular Graphs. Topics in Algebraic Graph Theory, Cambridge University Press, Cambridge (2004)

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway

    Andriy Bondarenko

  2. IST Austria, Klosterneuburg, Austria

    Anton Mellit

  3. Department of Mathematics, University of Manitoba, Winnipeg, MB, Canada

    Andriy Prymak

  4. International Centre for Theoretical Physics, Trieste, Italy

    Danylo Radchenko

  5. Humboldt University of Berlin, Berlin Mathematical School, Berlin, Germany

    Maryna Viazovska

Authors
  1. Andriy Bondarenko
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  2. Anton Mellit
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  3. Andriy Prymak
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  4. Danylo Radchenko
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  5. Maryna Viazovska
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Editor information

Editors and Affiliations

  1. School of Mathematics and Statistics, University of New South Wales, Sydney, Australia

    Josef Dick

  2. School of Mathematics and Statistics, University of New South Wales, Sydney, Australia

    Frances Y. Kuo

  3. Department of Computer Science, Columbia University, New York, USA

    Henryk Woźniakowski

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Bondarenko, A., Mellit, A., Prymak, A., Radchenko, D., Viazovska, M. (2018). There Is No Strongly Regular Graph with Parameters (460, 153, 32, 60). In: Dick, J., Kuo, F., Woźniakowski, H. (eds) Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan. Springer, Cham. https://doi.org/10.1007/978-3-319-72456-0_7

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