on the distance-transitivity of the folded hypercube

The folded hypercube f qn is the cayley graph cay(z n2, s), where s = {e1, e2, . . . , en} ∪ {u = e1 + e2 + · · · + en}, and ei = (0, . . . , 0, 1, 0, . . . , 0), with 1 at the ith position, 1 ≤ i ≤ n. in this paper, we show that the folded hypercube f qn is a distance-transitive graph. then, we study some properties of this graph. in particular, we show that if n ≥ 4 is an even integer, then the folded hypercube f qn is an automorphic graph, that is, f qn is a distance-transitive primitive graph which is not a complete or a line graph.