Abstract
We present a new non-existence proof for the strongly regular graph G with parameters (76, 21, 2, 7), using the unit vector representation of the graph.
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Notes
We thank the referee for pointing this out to us.
References
Brouwer, A.E., Haemers, W.H.: Spectra of Graphs. Universitext. Springer, New York (2012)
Dixmier, S., Zara, F.: Etude d’un quadrangle généralisé author de deux de ses point non liés (1976) (unpublished manuscript)
Godsil, C.D.: Algebraic Combinatorics. Chapman & Hall, New York (1993)
Haemers, W.H.: There exists no (76, 21, 2, 7) strongly regular graph. In: de Clerck, F., Beutelspacher, A. (eds.) Finite Geometry and Combinatorics: The Second International Conference at Deinze, London Mathematical Society Lecture Notes Series, pp. 175–176. Cambridge University Press, Cambridge (1993)
Humphreys, J.E.: Reflection Groups and Coxeter Groups. Cambridge University Press, Cambridge (1990)
van Lint, J.H., Brouwer, A.E.: Strongly regular graphs and partial geometries. In: Jackson, D.H., Vanstone, S.A. (eds.) Enumeration and Design, pp. 85–122. Academic Press, New York (1984)
Acknowledgements
The authors are grateful to King Fahd University of Petroleum and Minerals for supporting this research.
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Alfuraidan, M.R., Sarumi, I.O. & Shpectorov, S. On the Non-Existence of \(\mathrm{{srg}(76,21,2,7)}\). Graphs and Combinatorics 35, 847–854 (2019). https://doi.org/10.1007/s00373-019-02039-w
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DOI: https://doi.org/10.1007/s00373-019-02039-w