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The Hermitian adjacency matrix of a mixed graph with the vertex set $ \\{v_{1}, \\ldots , v_{n}\\} $, is the matrix $ H=[h_{ij}]_{n \\times n} $, where $ h_{ij}=-h_{ji}=i $ if there is a directed edge from $ v_{i} $ to $ v_{j} $, $ h_{ij}=1 $ if there exists an undirected edge between $v_i$ and $v_{j}$, and $h_{ij}=0$ otherwise. The Hermitian spectrum of a mixed graph is defined to be the spectrum of its Hermitian adjacency matrix. In this paper we study mixed graphs which are determined by their Hermitian spectrum (DHS). 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