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Keywords:
factor; $Q$-spectral radius; distance spectral radius; minimum degree
factor; $Q$-spectral radius; distance spectral radius; minimum degree
Summary:
For a set $\{A, B, C, \ldots \}$ of graphs, an $\{A, B, C, \ldots \}$-factor of a graph $G$ is a spanning subgraph $F$ of $G$, where each component of $F$ is contained in $\{A, B, C, \ldots \}$. 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 spectral radius for a graph involving minimum degree to guarantee the existence of a $\{K_2, \{C_k\}\}$-factor, respectively.
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