What insight does the H-R diagram provide regarding the physical factors separating stars far from the Main Sequence diagonal?

Answer

It graphically separates the effect of radius from the effect of temperature.

The Hertzsprung-Russell diagram plots temperature (the horizontal axis) against luminosity (the vertical axis). Stars clustered on the Main Sequence show a tight correlation between these two properties because fusion rate dictates both. However, stars that have evolved—Giants or White Dwarfs—deviate significantly. Their vertical displacement from the diagonal line clearly illustrates that in these evolved stages, stellar radius, which contributes through the $R^2$ term in the radiation law, becomes the dominant factor dictating their extreme luminosity relative to their measured temperature.

What insight does the H-R diagram provide regarding the physical factors separating stars far from the Main Sequence diagonal?
physicstemperaturestarLuminosityrelation