Over the past few decades, there have been a lot of activity about combining fixed point theory and another branches in mathematics such differential equations, geometry and algebraic topology. In 2005, Echenique started combining fixed point theory and graph theory by giving a short constructive proof for the Tarski fixed point theorem by using graphs. In 2006, Espinola and Kirk started combining fixed point theory and graph theory. Recently, this field have been of great interest for fixed point theorists. In this paper, we give some fixed point results for generalized quasi-contractive multifunctions on graphs.