A graph G is called integral if all the eigenvalues of its adjacency matrix are integers. In this paper, we investigate integral complete n-partite graphs. New sufficient conditions for a construction of integral complete n-partite graphs for integral complete r-partite graphs

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�are given. Further, using this construction, we can construct infinitely many new classes of integral complete n-partite graphs. Additionally, we found five new primitive integral complete 4‑partite graphs. These results are a new contribution to the search of such integral graphs.

integral complete n-partite graph, integral graph, n-partite graph.