A generalization of Wallis-Fon-Der-Flaass construction of strongly regular graphs
Mikhail Muzychuk
Netanya Academic College Department of Computer Science and Mathematics 1 University st. Netanya 42365 Israel
DOI: 10.1007/s10801-006-0030-7
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.
Pages: 169–187
Keywords: keywords strongly regular graphs; prolific construction
Full Text: PDF
References
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2. 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.
3. A. E. Brouwer, “Distance regular graphs of diameter 3 and strongly regular graphs,” Disc. Math. 49 (1984), 101-103.
4. 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.
5. P. Cameron, Parallelisms in Complete Designs, Cambridge Univ. Press, Cambridge, 1976.
6. P. Cameron and D. Stark, “A prolific construction of strongly regular graphs with the n-e.c. property,” Elec J. Combin. 9 (2002), #R31.
7. U. Dempwolff, “Primitive rank 3 groups on symmetric designs,” Des. Codes Cryptogr. 22 (2001), 191-207.
8. D.G. Fon-Der-Flaass, “New prolific constructions of strongly regular graphs,” Adv. Geom. 2(3) (2002), 301-306.
9. X.L. Hubaut, “Strongly regular graphs,” Discrete Math. 13 (1975), 357-381.
10. W.H. Haemers and V.D. Tonchev, “Spreads in strongly regular graphs,” Des. Codes Cryptogr. 8 (1996), 145-157. Springer
11. J.M. Goethels and J.J. Seidel, “Strongly regular graphs derived from combinatorial designs,” Canad. J. Math. 22 (1970), 597-619.
12. M. Klin, “Strongly regular graph on 96 vertices,” J. Geom. 65 (1999), 15-16.
13. 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.
14. W.D. Wallis, “Construction of strongly regular graphs using affine designs,” Bull. Austral. Math. Soc. 4 (1971), 41-49.