In the Hertzsprung-Russell Diagram, a star that falls under spectral class K and has a luminosity of \( 10^6 \) (or 1,000,000 times the luminosity of the Sun) would be classified as a red supergiant.
Red giants typically have lower luminosity than \( 10^6 \), while blue giants would be classified under a hotter spectral class (like O or B). White dwarfs have much lower luminosity and are not classified in spectral class K. Therefore, the correct response is:
red supergiant.