Characterizing star factors via the size, the spectral radius or the distance spectral radius of graphs

Let be a graph and let be an integer. A -factor of is a spanning subgraph of in which each component is isomorphic to a member in In this paper, we first establish a lower bound on the size (resp. the spectral radius) of to guarantee that contains a -factor. Then we determine an upper bound on the distance spectral radius of to ensure that has a -factor. Furthermore, we construct some extremal graphs to show all the bounds obtained in this contribution are best possible.