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For a set $\{A,B,C,...\}$ of graphs, an $\{A,B,C,...\}$-factor of a graph $G$ is a spanning subgraph $F$ of $G$, where each component of $F$ is contained in $\{A,B,C,...\}$. It is very interesting to investigate the existence of factors in a graph with given minimum degree from the prospective of eigenvalues. We first propose a tight sufficient condition in terms of the $Q$-spectral radius for a graph involving minimum degree to contain a star factor. Moreover, we also present tight sufficient conditions based on the $Q$-spectral radius and the distance...