Final answer:
A spectral class K star with the lowest luminosity on the H-R diagram would be a main-sequence star, falling in the category of spectral type V.
Step-by-step explanation:
Based on the characteristics of stars on the H-R (Hertzsprung-Russell) diagram, the type of star that belongs to spectral class K and has the lowest luminosity would be a main-sequence star. In the H-R diagram, main-sequence stars like our Sun are categorized as spectral type V. The categories of giants (III), supergiants (Ia, Ib, II), and white dwarfs occupy different positions on the H-R diagram based on their respective surface temperatures and luminosities. Class K main-sequence stars would be cooler and less luminous than the Sun (a G2 main-sequence star) and would be found on the lower part of the main sequence band.