Constraints on $\Lambda N$ Effective Interactions from Mirror Hypernuclei in a Deformed Relativistic Hartree-Bogoliubov Model

We investigate the ground-state properties of four mirror hypernuclei pairs--$^{10}_\Lambda$Be-$^{10}_\Lambda$B, $^{12}_\Lambda$B-$^{12}_\Lambda$C, $^{16}_\Lambda$N-$^{16}_\Lambda$O, and $^{40}_\Lambda$K-$^{40}_\Lambda$Ca--within the deformed relativistic Hartree-Bogoliubov framework, analyzing their connection to $\Lambda N$ effective interactions. Systematic calculations with eight distinct effective interactions reveal linear correlations between mirror hypernuclei in $\Lambda$ separation energies and charge radii. The charge symmetry breaking effects, quantified through $\Lambda$ separation energy differences, exhibit a positive correlation with the SU(3) flavor symmetry violation. We emphasize that constraints derived from $A=10$ and $A=12$ hypernuclear pairs must explicitly incorporate rotational energy correction effects. Precision measurements of the (near) spherical $A=16$ and $A=40$ mirror systems are proposed as critical benchmarks for refining the isospin part of the hyperon-nucleon interactions.