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 K_n 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 K₄₅ on 135 vertices is produced with the aid of a decoration of the alternating group A₆.