On the Number of Distinct Functional Graphs of Affine-Linear Transformations over Finite Fields

We study the number of non-isomorphic functional graphs of affine-linear transformations from (\F_q)^n to itself, and we prove upper and lower bounds on this quantity for n large. As a corollary to our result, we prove bounds on the number of conjugacy classes in the symmetric group S_{q^n} that intersect AGL_n(q).