Graphs and Combinatorics

, Volume 35, Issue 4, pp 847–854 | Cite as

On the Non-Existence of \(\mathrm{{srg}(76,21,2,7)}\)

  • Monther R. Alfuraidan
  • Ibrahim O. Sarumi
  • Sergey ShpectorovEmail author
Original Paper


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.


Strongly regular graph Distance regular graph Unit vector representation 

Mathematics Subject Classification

Primary 05E30 Secondary 05C30 



The authors are grateful to King Fahd University of Petroleum and Minerals for supporting this research.


  1. 1.
    Brouwer, A.E., Haemers, W.H.: Spectra of Graphs. Universitext. Springer, New York (2012)CrossRefzbMATHGoogle Scholar
  2. 2.
    Dixmier, S., Zara, F.: Etude d’un quadrangle généralisé author de deux de ses point non liés (1976) (unpublished manuscript)Google Scholar
  3. 3.
    Godsil, C.D.: Algebraic Combinatorics. Chapman & Hall, New York (1993)zbMATHGoogle Scholar
  4. 4.
    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)CrossRefGoogle Scholar
  5. 5.
    Humphreys, J.E.: Reflection Groups and Coxeter Groups. Cambridge University Press, Cambridge (1990)CrossRefzbMATHGoogle Scholar
  6. 6.
    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)Google Scholar

Copyright information

© Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsKing Fahd University of Petroleum and MineralsDhahranSaudi Arabia
  2. 2.School of MathematicsUniversity of BirminghamEdgbastonUK

Personalised recommendations