Fraudulence is the action or quality of cheating, lying, or deceiving someone. The fraudulence of an election might trigger a recount, or even an entirely new election.
Fraudulence is telling lies or hoaxing people in some way. One example of fraudulence might be pretending to be a police officer, and another is claiming to have the ability to communicate with people who have died, especially if you're taking money from relatives who hope to send them messages. Fraudulence comes from the Latin fraudulentia, from fraus, "cheating or deceit."