Relative difference sets fixed by inversion and Cayley graphs

Authors:
Yu Qing Chen;Cai Heng Li
Affiliations:
Department of Mathematics and Statistics, Wright State University, Dayton, OH and University of Western Australia;School of Mathematics and Statistics, The University of Western Australia, Crawley, WA 6009, Australia and Department of Mathematics, Ohio State University, Columbus, OH
Venue:
Journal of Combinatorial Theory Series A
Year:
2005

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Abstract

Using graph theoretical technique, we present a construction of a (30, 2, 29, 14)-relative difference set fixed by inversion in the smallest finite simple group--the alternating group A5. To our knowledge this is the first example known of relative difference sets in the finite simple groups with a non-trivial forbidden subgroup. A connection is then established between some relative difference sets fixed by inversion and certain antipodal distance-regular Cayley graphs. With the connection, several families of antipodal distance-regular Cayley graphs which are coverings of complete graphs are presented.