A new construction of antipodal distance regular covers of complete graphs through the use of Godsil-Hensel matrices - Klin, Mikhail (Ars mathematica contemporanea, 2011)
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 ?$n^2$? 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 ?$K_{45}$? on 135 vertices is produced with the aid of a decoration of the alternating group ?$A_6$?.
Keywords: antipodal graph; antipodni grafi; association scheme; automorphism group; combinatorics; conference matrix; Foster graph; generalized Hadamard matrix; Godsil-Hensel matrix; group ring; grupa avtomorfizmov; istance regular cover; kombinatorika; Mathieu group; Payne's doily; razdaljno regularen krov; resolvable transversal design; Schur multiplier; semibiplane; Taylor graph; Tutte's 8-cage; two-graph; Wielandt's 2-closure