Abstract
Let be a graph. An edge-coloring of is a function , where is a set of colors. Respect to a subgraph of is called a rainbow subgraph if all edges of get different colors. Graph is called rainbow connected if for every two distinct vertices of is joined by a rainbow path. The rainbow connection number of , denoted by , is the minimum number of colors needed in coloring all edges of such that is a rainbow connected. The main problem considered in this thesis is determining the rainbow connection number of graph. In this thesis, we determine the exact value of the rainbow connection number of some classes of graphs such as Cycles, Complete graph, and Tree. We also determining the lower bound and upper bound for the rainbow connection number of graph.
 Keywords: Rainbow Connection Number, Graph, Edge-Coloring on Graph.
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