Relative difference sets fixed by inversion and Cayley graphs

Journal of Combinatorial Theory. Series A

Volumn 111, Issue 1, 2005, Pages 165-173

  Chen, Yu Qing ^a   Li, Cai Heng ^b,c  

^a WRIGHT STATE UNIVERSITY   (United States)

^b UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

^c OHIO STATE UNIVERSITY   (United States)

Author keywords

Cayley graph; Distance regular graph; Relative difference set

Indexed keywords

EID: 20344379659     PISSN: 00973165     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcta.2004.09.007     Document Type: Article

References (24)

1. K.T. Arasu D. Jungnickel A. Pott Divisible difference sets with multiplier - 1 J. Algebra 133 1990 35-62
2. A.E. Brouwer A.M. Cohen A. Nemaier Distance-Regular Graphs 1989 Springer Berlin-New York
3. T. Beth, D. Jungnickel, H. Lenz, Design Theory, vol. 1, 2nd edition, Cambridge University Press, Cambridge, 1999.
4. R.C. Bose An affine analogue of Singer's theorem, J. Indian Math. Soc. 6 1942 1-15
5. A.T. Butson Relations among generalized Hadamard matrices, relative difference sets and maximal length linear recurring sequences, Canad. J. Math. 15 1963 42-48
6. Y.Q. Chen On the existence of abelian Hadamard difference sets and a new family of difference sets, Finite Fields Appl. 3 1997 234-256
7. Y.Q. Chen, K.J. Horadam, W-H. Liu, Relative difference sets fixed by inversion (II) - character theoretical approach, J. Combin. Theory Ser. A, to appear.
8. Y.Q. Chen, K.J. Horadam, W-H. Liu, Relative difference sets fixed by inversion (III) - Cocycle theoretical approach, Discrete Math., to appear.
9. J. Davis J. Jedwab A unifying construction for difference sets, J. Combin. Theory Ser. A 80 1997 13-78
10. J.E. Elliott A.T. Butson Relative difference sets, Illinois J. Math. 10 1966 517-531
11. C.D. Godsil A.D. Hensel Distance regular covers of complete graphs, J. Combin. Theory Ser. B 56 1992 205-238
12. A.D. Hensel, Antipodal distance regular graphs, Master's Thesis, University of Waterloo, 1988.
13. C.W.H. Lam On relative difference sets, Congr. Number 20 1977 445-474
14. K.H. Leung S.L. Ma Constructions of partial difference sets and relative difference sets on p-groups, Bull. London Math. Soc. 22 1990 533-539
15. K.H. Leung S.L. Ma V. Tan Abelian divisible difference sets with multiplier - 1, J. Combin. Theory Ser. A 59 1992 51-72
16. C.H. Li Finite CI-group are soluble, Bull. London Math. Soc. 31 1998 419-423
17. C.H. Li On isomorphisms of finite Cayley graphs - a survey, Discrete Math. 256 2002 303-334
18. C.H. Li Finite s-arc transitive Cayley graphs and flag-transitive projective plane, Proc. Amer. Math. Soc. 133 2005 31-41
19. C.H. Li, Finite edge transitive graphs and rotary Cayley maps, Trans. Amer. Math. Soc., to appear.
20. S.L. Ma Reversible relative difference sets, Combinatorica 12 1992 425-432
21. A. Pott Finite Geometry and Character Theory 1995 Springer New York
22. A. Pott, A survey on relative difference sets, Groups difference sets, and the Monster (Columbus, OH, 1993), Ohio State University Mathematical Research Institute Publication, vol. 4, de Gruyter, Berlin, 1996, pp. 195-232.
23. B. Schmidt Cyclotomic integers and finite geometry, J. Amer. Math. Soc. 12 1999 929-952
24. C.D. Godsil R.A. Liebler C.E. Praeger Antipodal distance transitive covers of complete graphs, European J. Combin. 19 1998 455-478