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

Mikhail Klin, Christian Pech

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

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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DOI: https://doi.org/10.26493/1855-3974.191.16b

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications