Abstarct: The Voronoi diagram is an interesting construction in computational geometry, which has many applications in other sciences. This diagram is a way of dividing the page into a number of areas, so that these areas have certain conditions and satisfy certain constraints. In this thesis, after introducing the Voronoi diagram, we describe the complexity of this diagram on the graphs and then express the methods of finding the Voronoi diagram on trees and graphs. Some applications of voronoi diagrams are also mentioned in this thesis.