A new construction of antipodal distance regular covers of complete graphs through the use of Godsil-Hensel matrices
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 K45 on 135 vertices is produced with the aid of a decoration of the alternating group A6.
Antipodal graph, automorphism group, association scheme, conference matrix, distance regular cover, generalized Hadamard matrix, Godsil-Hensel matrix, group ring, Foster graph, Mathieu group, Payne's doily, resolvable transversal design, Schur multiplier