A new construction of antipodal distance regular covers of complete graphs through the use of Godsil-Hensel matrices

Abstract

New constructions of regular distance regular antipodal covers (in the sense of Godsil- Hensel) of complete graphs Kn are presented. The main source of these constructions are skew generalized Hadamard matrices. It is described how to produce such a matrix of order n2 over a group T from an arbitrary given generalized Hadamard matrix of order n over the same group T. Further, a new regular cover of K 45on 135 vertices is produced with the aid of a decoration of the alternating group A6. Copyright © 2011 DMFA Slovenije.