If you are not having sex with those they accuse you of, it is best you just ignore them. Because only you, the people involved by mouth and God knows what is and isn't true. Unless these accusations are gravely affecting your interpersonal relationships such as your career, and other areas of importance, then all you can do is talk to the people who are spreading these rumors. See if you can come to an understanding what is the problem and why these rumors are spreading.
If they appear to have no logical reason as to why this is spreading, then sadly, you may have to see if you have a legal case and show evidence that it is affecting you. Such as suspension or job loss. Try to avoid any legal matters that are not necessary. Whether you related or not, the question is is it true meaning that these sexual acts were going on between the people involved? If so, then unless it is people's business, then if they are not related and nothing happened, it is not their personal business. It should not be a joke about incest or anybody having a sexual relationship with anybody. It simply shouldn't be anyone's business unless a warrant of concern. This just sounds like something that needs to be presented as a warning to those spreading it.
Honestly you should do some research on your own rather than just take our word for it but I’m pretty sure that’s like defamation of character..
It is defamation of character, especially through character reference that goes against your morals. For example. Everybody who knows me knows I am not having sex before marriage or got involved with a guy before. If rumors spread that I am dating a person, and I had that happened to me before, I can say defamation of character because I made a decision to not date anybody. If somebody lied and said I had sex with a guy, then they better have proof like my bed sheet or something, because I know I am a virgin and medical examination would prove it also. Regardless if it is anyone's business or not, if you stand strong on your morals, no lie will win over the truth.
Thanks for verifying that, I wasn’t sure if defamation of character was the right thing and didn’t want to pass on the wrong info, I’m no where near savvy with legal stuff lol
Neither am I. But just because you are not versed in it, it doesn't mean you shouldn't learn it. I rather no my rights than being ignorant.
Unless it affects your mental or professional health and its false you can't.
Scroll Down to Read Other Opinions
What's Your Opinion? Sign Up Now!
Sexual Relationships 
Sexual Health 
Superb Opinion