A Liger is the offspring of a male Lion and a female Tiger or Tigress. If the parents were a male Tiger and a female Lion or Lioness then the offspring would be known as a Tiglon or Tigon. To answer your 2nd question; it’s no, Ligers aren’t so large as a result of hybrid vigor. read more
It has to do with the weirdness that occurs when you hybridize across two lineages which have been distinctive for millions of years, but not so long so as not to be able to produce viable offspring (in fact, many ligers are fertile as well). read more