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Let G be a \((p,q)\)-graph with p vertices and q edges. An edge-labeling assignment \(\text{L : E} \to \text{N}\) is a map which assigns a positive integer to each edge in E. The induced map \(\text{L}^+ : \text{V} \to \text{N}\) defined by \(\text{L}^+\text{(v)} = \Sigma\{\text{L(u,v) : for all (u,v) in E}\}\) is called the vertex sum. The edge labeling assignment is called \underline{magic} if \(\text{L}^+\) is a constant map. If L is a bijection with \(\text{L(E)} = \{1,2,\ldots,\text{q}\}\) and L is magic then we say L is supermagic. B. M. Stewart showed that \(\text{K}_5\) is not supermagic and when \(\text{n} \equiv 0 \pmod{4}\) , \(\text{K}_\text{n}\) is not supermagic. In this paper, we exhibit supermagicness for a class of regular complete k-partite graphs.