In this work, we systematically investigate the favored α-decay half-lives and α preformation probabilities of both odd- A and doubly-odd nuclei related to ground and isomeric states around the doubly magic cores at Z=82, N=82 and at Z=82, N=126, respectively, within a two-potential approach from the view of the valence nucleon (or hole). The results show that the α preformation probability is linearly related to NpNn or NpNnI, where Np, Nn, and I are the number of valence protons (or holes), the number of valence neutrons (or holes), and th...