Rainbow connection number of Connected Graph

A path of a connected graph is rainbow if no two edges of it are colored the same. An edge-coloring graph is rainbow connected if a rainbow path connects any two vertices. An edge coloring under which is rainbow connected is called a rainbow coloring. The rainbow connection number of a connected graph , denoted by , as the smallest number of colors that are needed in order to make rainbow connected. In this paper, we construct different type of connected graph and determine the exact value of for them.