Transposed Poisson structures on Virasoro-type algebras

We compute $\frac{1}{2}$-derivations on the deformed generalized Heisenberg-Virasoro algebras and on not-finitely graded Heisenberg-Virasoro algebras ${\widehat{W}}_n(G)$, ${\tilde{W}}_n(G)$, and ${\widetilde{HW}}_n(G)$. We classify all transposed Poisson structures on such algebras.