Eigenvalues and component factors in graphs

For a set H of connected graphs, an H-factor of G is a spanning subgraph F of G if each component of F is isomorphic to an element of H. Kano, Lu and Yu [Electron. J. Combin. 26 (2019) P4.33] provided a good characterization based on an isolated vertex condition for the existence of a 1,1,K1,2,…,K1,k, T(2k+1)\-factor in graphs. Motivated by the above elegant result, we in this paper focus on the existence of a 1,1,K1,2,…,K1,k, T(2k+1)\-factor in graphs from perspective of eigenvalues. By adopting a crucial technique due to Tait [J. Combin. Theory Ser. A 166 (2019) 42-58] and combining typical spectral methods and structural analysis, we present tight sufficient conditions in terms of the spectral radius and the distance spectral radius for a graph to contain a 1,1,K1,2,…,K1,k, T(2k+1)\-factor, respectively.