On D. G. Higman's note on regular 3-graphs

Authors

  • Daniel Kalmanovich Ben-Gurion University of the Negev, Israel

DOI:

https://doi.org/10.26493/1855-3974.243.260

Keywords:

Antipodal graph, association scheme, distance regular graph of diameter 3, Godsil-Hensel matrix, group ring, Taylor graph, two-graph.

Abstract

We introduce the notion of a t-graph and prove that regular 3-graphs are equivalent to cyclic antipodal 3-fold covers of a complete graph. This generalizes the equivalence of regular two-graphs and Taylor graphs. As a consequence, an equivalence between cyclic antipodal distance regular graphs of diameter 3 and certain rank 6 commutative association schemes is proved. New examples of regular 3-graphs are presented.

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Published

2012-05-31

Issue

Vol. 6 No. 1 (2013)

Section

Special Issue Bled'11

License

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