A classification of one-dimensional affine rank three graphs

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Abstract

The rank three subgroups of a one-dimensional affine group over a finite field were classified in 1978 by Foulser and Kallaher. Although one can use their results for a classification of corresponding rank three graphs, the author did not find such a classification in a literature. The goal of this note is to present such a classification. It turned out that graph classification is much simpler than the group one. More precisely, it is shown that the graphs in the title are either the Paley graphs or one of the graphs constructed by Van Lint and Schrijver or by Peisert. Our approach is based on elementary group theory and does not use the classification of rank three affine groups.

Original languageEnglish
Article number112400
JournalDiscrete Mathematics
Volume344
Issue number7
DOIs
StatePublished - 1 Jul 2021

Keywords

  • Affine group
  • Rank three graph

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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