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 Construction of full H-matrices with the given eigenvalues based on the Givens matrices Keywords:Full matrix; H-matrix; Strictly diagonally dominant matrix; $\alpha$-strictly diagonally dominant matrix; $\alpha$-double strictly diagonally dominant matrix, Givens matrix. Abstract: The inverse eigenvalue problem is about how to construct a desired matrix whose spectrum is the given number set. In this paper, in view of the Givens matrices, we prove that there exist three classes of full H-matrices which include strictly diagonally dominant full matrix, $\alpha$-strictly diagonally dominant full matrix and $\alpha$-double strictly diagonally dominant full matrix, and their spectrum are all the given number set. In addition, we design some numerical algorithms to explain how to construct the above-mentioned full H-matrices.