  Star polymer is a typical nonlinear macromolecule possessing special
thermodynamic behaviors for the existence of a jointing point. The
thermodynamic transitions of a single star polymer are systematically studied
with bond fluctuation model using Wang-Landau sampling technique. A new
analysis method applying the shape factor is proposed to determine coil-globule
(CG) and liquid-crystal (LC) transitions, which shows higher efficiency and
precision than canonical specific heat function. It is found that the LC
transition of star polymer at lower temperature obeys the identical scaling law
as linear polymer. With the increase of the arm density of star polymer,
however, the CG transition point, corresponding to {\theta} temperature, shifts
towards the LC transition and the reason comes from the high density arms of
star polymer, which requires the lower temperature for attracting force to
overcome the volume excluding effects of chain. This work clearly demonstrates
that the distinction of linear and star polymers in structures only affects CG
transition and has no influence on LC transition.
