The rainbow connection number of a graph G, denoted rc(G), is the smallest number of colors needed to color the edges of G so that any two vertices are connected by a path whose edges all have different colors. Similarly we define the strong rainbow connection number of G, denoted by src(G), by replacing "path" with "geodesic". n this paper, we study the rc and src of a very specific construction known as splitting. For any graph H and any m ∈ N, its m-splitting is a new graph denoted by Spl_m(G) constructed as follows. Suppose V(H)= {h_1: ...,h_n}. Then for each h_t we introduce m new vertices v_i~1,..., v_i~m and we join each new vertex v_i~1 to all neighbors of the original vertex h_t in H. In this paper we determine the rc and src of Spl_m(P_3) for all m ∈ N, where P_3 is the 3-path, i.e. path with three vertices.
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