In this paper, the author considers the action of G+PSL(n, p) (n ≥ 3, p is an odd prime, and (n, p–1) = 1) on the set of frames of the projective space PG(n–1, p) over the field GF(p), and survey the non-self-paired orbitals of G. Then the author finds an infinite family of vertex-primitive 1/2-transitive graphs. In addition, the author obtains a method of computing the suborbits of PSL(n, p) acting on the frame-set of PG(n–1, p).
