(in the MK system, a “luminosity class” is added to the spectral class using “roman numerals”)
This is based on the width of certain absorption lines in the star’s spectrum, which vary with the density of the atmosphere and so distinguish giant stars from dwarfs. Luminosity class 0 or Ia+ stars for hypergiants, class I stars for supergiants, class II for bright giants, class III for regular giants, class IV for sub-giants, class V for main-sequence stars, class sd for sub-dwarfs, and class Dfor white dwarfs.
(the full spectral class for the sun is then G2V, indicating a main-sequence star with a temperature around 5,800 K)