  The extended bigraded Toda hierarchy (EBTH) is an integrable system satisfied
by the total descendant potential of $\mathbb{CP}^1$ with two orbifold points.
We construct additional symmetries of the EBTH and describe explicitly their
action on the Lax operator, wave operators, and tau-function of the hierarchy.
In particular, we obtain infinitesimal symmetries of the EBTH that act on the
tau-function as a subalgebra of the Virasoro algebra, generalizing those of
Dubrovin and Zhang.
