LET G BE A GRAPH AND A BE AN ABELIAN GROUP. A GRAPH G IS CALLED A -MAGIC IF THERE EXISTS AN EDGE LABELING (FORMULA). G SUCH THAT THE INDUCE VERTEX SET LABELING (FORMULA), DEFINE BY (FORMULA), WHERE THE SUM IS OVER ALL EÎ E(G), IS A CONSTANT MAP. A CONSTANT OF A MAGIC SUM IS CALLED AN INDEX OF G, AN INDEX FOR SHORT, AND WE WRITE I A (G) =(FORMULA) -MAGIC WITH INDEX RG. IN THIS PAPER FOR T ³ 2 WE DETERMINE THE INDEX SET OF THE COMPLETE MULTIPARTITE GRAPH KN1,…, NT, WHERE NI >2 (I=1,…, T).