The Harvard classification only takes into account the effect of the temperature on the spectrum. It is found that two stars with the same effective temperature may have widely different luminosities. Thus for a more precise classification, one has to take into account the luminosity of the star. A new classification is introduced by Morgan, Keenan and Kellman (known as MKK) called Yerkes spectral classification. In this classification six different luminosity classes are proposed.
Ia: most luminous super giant
Ib: less luminous super giant
II: luminous giants
III: sub giants
IV: normal giants
V: main sequence stars
The luminosity class is determined from spectral lines that depend strongly on the stellar surface gravity which is closely related to the luminosity.
The masses of giants and dwarfs are roughly similar but the radii of giants are much larger than those of dwarfs. Therefore, the gravitational acceleration 
at the surface of the giant is much smaller than for a dwarf. Due to this the gas density and the pressure in the atmosphere of a giant is much smaller. because of this luminosity effects can be seen.
Examples:
Proxima century: M5.5V
Sirius A: A1V
Alpha Century B: K1V
Capella Aa: G5III
AB Doradas: K1III
Deneb: A2Ia
Spica: B1III
Betelgeuse: M2Ib
Polaris: F7II
