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

Daniel Kalmanovich

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.

Keywords


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

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

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