Symmetry of the boundary-neighborhood regularity property

Determine whether, for strongly regular graphs with parameters (n,k,lambda,mu), attaining an upper or lower bound from Theorem \ref{thm:main} for an induced regular subgraph L necessarily implies that the corresponding set R also attains its own upper or lower bound.

Background

Theorem \ref{thm:main} guarantees uniform neighborhood counts from M into L and from R into M when an extremal value is attained. For the parameter set (99,14,1,2), computer searches found that every extremal L examined had a corresponding extremal R. The paper leaves open whether this phenomenon is specific to those parameters or holds for general strongly regular graphs.

References

For $n=99,k=14,\lambda=1,\mu=2$, a computer search showed that every $L$ meeting its upper or lower bound resulted in an $R$ meeting its own upper or lower bound. Will this hold for other values of $n, k, \lambda$, or $\mu$?

— An Induced Subgraph Paradigm for Strongly Regular Graph Constructions  (2610.22299 - Baker, 15 Oct 2026) in Section 6, Further Work