Overlap of quartic bicirculant nut-graph classes

Determine whether any quartic bicirculant nut graphs, beyond the two families identified in Proposition 6.1, belong simultaneously to more than one of the classes B1, B2, and B3.

Background

The paper classifies quartic bicirculant nut graphs within four parameter classes, B1, B2, B3, and B4, and observes that these classes are not disjoint. Proposition 6.1 identifies two families of overlaps: graphs shared by B1 and B2, and graphs shared by B2 and B3; both families are also circulant nut graphs. The computational data summarized in Table 1 motivate the unresolved question of whether further overlaps exist beyond these two explicitly described families.