Same-parameter strongly regular graphs with different VC-dimensions

Construct two strongly regular graphs with the same parameters and different VC-dimensions.

Background

The authors report that their computer search found no pair of strongly regular graphs with identical parameters but different VC-dimensions, although they see no reason such a pair cannot exist. They explicitly identify finding such a pair as an open problem and note that even the minimum order of two such graphs is unknown.

References

Several natural open problems bear mentioning. We no not expect the following problem to be difficult, but we do not know the minimum order of two such graphs. Find two strongly regular graphs with the same parameters and different VC-dimensions.

— The VC-dimension of strongly regular graphs  (2609.10330 - Byrne et al., 9 Sep 2026) in Section 8, Conclusion