The relationship between a main sequence star's b-v color value and luminosity is a direct relationship.
The Hipparcos satellite measures the distances between hundreds of thousands of stars. It measures the magnitude of each stars through two filters which are, a blue filter, yielding for B magnitude (for blue) and a greenish filter, yielding a V magnitude (for visual).
The difference between the B and V magnitude of star is (B-V) color , or sometimes just "color" in short. The wavelength of light where the star is related to the star's temperature, i.e., the hotter the star the more blue it is and the cooler the star the more red it is.
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