An edge-coloring of a graph is called rainbow if any two vertices are connected by a path consisting of edges of different colors. The least number of colors in such a coloring is called the rainbow connection number of G , denoted by rc( G ). An edge-coloring of a graph is called strong rainbow if any two vertices are connected by a geodesic consisting of edges of different colors. The least number of colors in such a coloring is called the strong rainbow connection number of G , denoted by src( G ). In this paper we study the rc and src of the m -splitting of a graph. In particular we study Spl m ( K n ). We present the exact values of its rc and src in several cases, and we prove several bounds in the other cases.
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