On the Rainbow Connection Number for Snowflake Graph

Let G be an arbitrary non-trivial connected graph. An edge-colored graph G is called a rainbow connected if any two vertices are connected by a path whose edges have distinct colors, such path is called a rainbow path. The smallest number of colors required to make G rainbow connected is called the rainbow connection number of G, denoted by rc(G). A snowflake graph is a graph obtained by resembling one of the snowflake shapes into vertices and edges so that it forms a simple graph. Let  be a generalized snowflake graph, i.e., a graph with  paths of the stem,  pair of outer leaves,  middle circles, and  pairs of inner leaves. In this paper we determine the rainbow connection number for generalized snowflake graph