What are you talking about? What we want is for Vulcan's star to have low UV emissions (relative to Sol) to explain why its desert-dwellers don't need a lot of melanin. It was not an "assumption," it was an informed conclusion based on the evidence I just provided you. Since I've already shown my work, already demonstrated the reasons why I drew that conclusion, you have no grounds for calling it an "assumption." Which should tell anyone with a decent high school education in astronomy that it's probably weaker in ultraviolet than the Sun. Although maybe I'm giving modern American high schools too much credit. Neither of which has anything to do with its UV output specifically. Again, 90% of stars are cooler and redder than Sol. But of course a planet can be closer to its star than Earth is; a planet around a red star would have to be closer to have liquid-water temperatures. So as seen from such a planet, the sun would be larger in the sky than Sol is and could be just as bright. And of course hotness is a function of how close a planet is to its star -- and how much infrared radiation the atmosphere traps with the greenhouse effect. UV output is a separate question.