Giants are designated III, supergiant I and white dwarfs have no special designation. Such designation I, III and V are called luminosity classes. So a G2III star would be a giant exhibiting G2 spectral signature. Dwarfs, giants, supergiants and white dwarfs represent different stages of stellar evolution. These are the variable stars.
Variable stars are stars whose luminosity varies with time as the star pulsates.
In particular there is a class of variable star known as Cepheid Variables . The stars vary by about one magnitude over periods ranging from one to 100 days. This strip lies up above the main sequence near the giant region. Stars that are in the instability region of the HR diagram tend to expand and contract as the surface layers heat and cool. This allows the variable star to be used as a tool for distance determination.