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

Authors

  • Mikhail Klin Ben-Gurion University of the Negev, Israel
  • Christian Pech Germany

DOI:

https://doi.org/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

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.

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Published

2011-02-14

Issue

Vol. 4 No. 2 (2011)

Section

GEMS 2009 - Tale, Slovakia

License

Articles in this journal are published under Creative Commons Attribution 4.0 International License
https://creativecommons.org/licenses/by/4.0/