  The presence of massive gravitons in the field of massive gravity is
considered as an important factor in investigating the structure of compact
objects. Hence, we are encouraged to study the dark energy star structure in
the Vegh's massive gravity. We consider that the equation of state governing
the inner spacetime of the star is the extended Chaplygin gas, and then using
this equation of state, we numerically solve the Tolman-Oppenheimer-Volkoff
(TOV) equation in massive gravity. In the following, assuming different values
of free parameters defined in massive gravity, we calculate the properties of
dark energy star such as radial pressure, transverse pressure, anisotropy
parameter, and other characteristics. Then, after obtaining the maximum mass
and its corresponding radius, we compute redshift and compactness. The obtained
results show that for this model of dark energy star, the maximum mass and its
corresponding radius depend on the massive gravity's free parameters and
anisotropy parameter. These results are consistent with the observational data,
and cover the lower mass gap. We also demonstrate that all energy conditions
are satisfied for this model, and in the presence of anisotropy, the dark
energy star is potentially unstable.
