Sufficient conditions on the existence of factors in graphs involving minimum degree

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 spectral radius for a graph involving minimum degree to guarantee the existence of a {K₂, {C_k}}-factor, respectively.