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In this paper, we used the permutation group together with the concept of cordiality in graph theory to introduce a new method of labeling. This construed permuted cordial labeling can be applied to all paths, cycles, fans and wheel graphs. Moreover, some other properties are investigated and show that the union of any two paths and the union of any two cycles are permuted cordial graphs. In addition, we investigated the permuted cordiality for the union of any path with cycle.