In short, Dwarf stars are normal, main sequence stars compared to the giants of the universe such as UY Scuti. The term Dwarf Star was created by Ejnar Hertzsprung to distinguish between the two different types of Red Stars, those that are giant stars such as Antares and those that are much smaller such as Proxima Centauri. Hertzsprung who along with Henry Norris Russell created the famous Hertzsprung-Russell star size map.
The star map shows the Sun as being in the middle, the sun is classed as a Yellow Dwarf star because although it is one of the larger stars in the galaxy, it is tiny to compared to UY Scuti, the currently recognised largest star in the milky way which when you discover that UY Scuti is over 1,700 times as big as the Sun, you can see why the Sun is called a Yellow Dwarf star.
When it comes to size of a star, size matters, it is best to be small rather than large because the smaller stars convert their hydrogen to helium at a slower rate than larger stars and will live longer. Our Sun is expected to die in about 5 billion years, that's so long in the future, we don't need to worry about. When we move and if we ever do move to another planet, we should find a planet orbiting a red dwarf as they will last for possibly trillions of years.
When stars use up their hydrogen, you'd think that they'd begin to shrink, instead the opposite is true. As a star uses up it fuel, the outward pressure overpowers gravity and they expand outwards. Betelgeuse was probably a normal star until it finished its main sequence and then expanded outwards to the size it is today.
A Dwarf Star will generally have a spectral type that V, VI, VII. There aren't that many stars that have VI or VII spectral type, most dwarf stars will just be V without any I beforehand.
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