Classification of strongly regular bicirculants and tricirculants

Classify strongly regular bicirculants and tricirculants, extending the existing structural results and constructions beyond the cases currently understood.

Background

The paper studies 3-isoregularity among strongly regular multicirculants, focusing especially on bicirculants and tricirculants. Although strongly regular circulants are classified, the corresponding theory for bicirculants and tricirculants remains incomplete. The authors identify this incomplete classification as an unresolved area motivating their results on non-existence of 3-isoregular examples under various order restrictions.

References

While everything is known about strong regularity of circulants (see [4]), the situation with bicirculants and tricirculants is still quite open, save for some structural results and some constructions (see [11, 25, 26, 28]).

— On 3-isoregularity of multicirculants  (2501.18217 - Kutnar et al., 30 Jan 2025) in Section 1, introductory remarks, p. 2