Do violet potatoes contain more or less solanine than normal potatoes? What is the solanine content of the violet potatoes? Is it more or less than in the normal potatoes?

Seems to be about the same.

In Effect of Genotype and Environment on the Glycoalkaloid Content of Rare, Heritage, and Commercial Potato Varieties, Tables 1 and 2 list 60 different potato varieties showing glycoalkaloid concentration (solanine and chaconine are shown separately); Table 1 indicates the skin color, and Table 2 indicates the flesh color. "Violet" is not an option, but "Blue" is, and there doesn't seem to be any particular correlation between skin or flesh color and glycoalkaloid concentration. (The potato with the highest concentration of glycoalkaloid in the flesh was a blue one, but other blue varieties were fairly low; the variety with the highest in the skin was "yellow".)