\label{fig:Prop}
Propagation diagram for a magnetized red giant model. The model has $M = 1.6 \, M_\odot$, $R =6.6 \, R_\odot$, ${\nu}_{\rm max} = 120 \, {\rm {\mathrm{\mu}}Hz}$, and a core magnetic field of $\approx 6 \times 10^6 \,{\rm G}$ (see Fig. \ref{Fig:Struc}). ({\bf A}) The red, blue, and green lines are the dipole Lamb frequency $L_1$, the buoyancy frequency $N$, and the magneto-gravity frequency $\omega_{\rm MG}$ (defined in Eqn. \ref{eqn:maggrav}), respectively. Regions are colored by the types of waves they support: the red region is the acoustic wave cavity, the blue region is the magneto-gravity wave cavity, and the green region hosts only Alfv\'en waves. The horizontal line is the frequency of maximum power, $\nu_{\rm max}$, for this stellar model. Waves at this frequency behave like acoustic waves near the surface, magneto-gravity waves in the outer core, and Alfv\'en waves in the inner core. ({\bf B}) Critical radial magnetic field strength $B_c$ needed to suppress dipole modes. $B_c$ (Eqn. \ref{eqn:Bc}) is evaluated at the angular frequency $\omega \! = \! 2 \pi \nu_{\rm max}$. $B_c$ has a sharp minimum at the H-burning shell, which determines the minimum field strength $B_{c,{\rm min}}$ required for dipole mode suppression.