Abstract: For G a finite group, F an algebraically closed field and W a faithful FG-module, the McKay graph, M_F(G, W), is a directed graph on the set of simple FG-modules. There is an edge in the graph from V_1 to V_2 if V_2 occurs as a composition factor of the tensor product of V_1 and W. These graphs famously come up in the McKay correspondence which says that such graphs for the group SU_2(C) are affine Dynkin diagrams of type A, D or E. In the case where the characteristic of F divides the order of G, finding the composition factors of tensor products is a hard problem. However it might surprise you to know that taking G to be SL_n(F_p) and W the standard n-dimensional module over the algebraic closure of F_p, we can show that the diameter of the McKay graph is (p − 1)(n^2 − n)/2. We are able to prove this neat formula without explicitly constructing the graphs. This is of particular interest to people looking at mixing times for random walks on McKay graphs.