I noticed the American Green Party Candidate for the 2012 Presidential Elections is also the candidate for the Socialist Party. This made me wonder: Is Liberal Green Politics a movement of Socialism?

yes, since socialism means putting the business under public control so the won't:
1) hire as few people as possible so they will demand less wage for their family need then use the lack of job to justify destroying the environment
2) make what the rich want but not what the poor need since they don't have money to invest in, thereby raising the poverty line
3) pretend to be green to trick others into buying wasteful things