I started dating the girl in my class and there have been rumors that im dating another girl but its not true will she break up with me and how do i squash the rumor
Just be honest to your girlfriend, I'm sure she has no reason to believe rumors. They exist, and they can be brutal and undermining, but as long as she knows, I'm sure it won't matter. And try to counter the rumor with truth by telling people yourself.
Um, make it very clear to her that you aren't dating anyone else, then just don't go flirting with other girls. It doesn't matter what other people say, so long as those around you know the truth.
Good up to the person who's making the rumor to stop. If you don't know who's making the rumor then tell a bunch of people that the rumor isn't true. Soon the truth will pass on.