Geodesic
A new construction of antipodal distance regular covers of complete graphs through the use of Godsil-Hensel matrices
Ars Mathematica Contemporanea, Tome 4 (2011) no. 2, pp. 205-243.

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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.
DOI : 10.26493/1855-3974.191.16b
Keywords: 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 
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Mikhail Klin; Christian Pech. A new construction of antipodal distance regular covers of complete graphs through the use of Godsil-Hensel matrices. Ars Mathematica Contemporanea, Tome 4 (2011) no. 2, pp. 205-243. doi : 10.26493/1855-3974.191.16b. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.191.16b/

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