Abstract
In this paper the Wallis-Fon-Der-Flaass construction of strongly regular graphs is generalized. As a result new prolific series of strongly regular graphs are obtained. Some of them have new parameters.
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References
R.A. Bailey, “Orthogonal partitions in designed experiments,” Des. Codes Cryptogr 8 (1996), 45–77.
A.E. Brouwer, J.H. Koolen, and M.H. Klin, “A root graph that is locally the line graph of the Petersen graph,” Disc. Math. 264 (2003), 13–24.
A. E. Brouwer, “Distance regular graphs of diameter 3 and strongy regular graphs,” Disc. Math. 49 (1984), 101–103.
A.E. Brouwer and J.H. van Lint, “Strongly regular graphs and partial geometries,” in: Enumeration and Designs, (eds.) D.M. Jackson and S.A. Vanstone, Academic Press, 1984, pp. 85–122.
P. Cameron, Parallelisms in Complete Designs, Cambridge Univ. Press, Cambridge, 1976.
P. Cameron and D. Stark, “A prolific construction of strongly regular graphs with the n-e.c. property,” Elec J. Combin. 9 (2002), #R31.
U. Dempwolff, “Primitive rank 3 groups on symmetric designs,” Des. Codes Cryptogr. 22 (2001), 191–207.
D.G. Fon-Der-Flaass, “New prolific constructions of strongly regular graphs,” Adv. Geom. 2(3) (2002), 301–306.
X.L. Hubaut, “Strongly regular graphs,” Discrete Math. 13 (1975), 357–381.
W.H. Haemers and V.D. Tonchev, “Spreads in strongly regular graphs,” Des. Codes Cryptogr. 8 (1996), 145–157.
J.M. Goethels and J.J. Seidel, “Strongly regular graphs defined from combinatorial designs,” Can J. Math. 22 (1970), 597–619.
M. Klin, “Strongly regular graph on 96 vertices,” J. Geom. 65 (1999), 15–16.
D.K. Ray-Chaudhuri and R.M. Wilson, “Solution of Kirkman's school-girl problem,” Proc. Symp. Pure Math. 19, AMS, Providence R.I. (1971), 187–203.
W.D. Wallis, “Construction of strongly regular graphs using affine designs,” Bull. Austral. Math. Soc. 4 (1971), 41–49.
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The author was partially supported by the Israeli Ministry of Absorption.
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Muzychuk, M. A generalization of Wallis-Fon-Der-Flaass construction of strongly regular graphs. J Algebr Comb 25, 169–187 (2007). https://doi.org/10.1007/s10801-006-0030-7
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DOI: https://doi.org/10.1007/s10801-006-0030-7