Summary: Lam and Van Lint, in their generalization of the Friendship Theorem, construct a kind of directed graphs with unique paths of fixed length, here denoted by D(c,k), and have proved that the automorphism group for D(c,k) contains a dihedral group of order \(2(c+1)\). The author has proved that the dihedral group is just the full automorphism group for D(c,k), using the properties of the adjacency matrix of D(c,k). Hence, a problem left over in Lam and Van Lint’s work has been solved.