On the distance-transitivity of the folded hypercube.

The folded hypercube FQn is the Cayley graph Cay(Z2n, 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 FQn 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 FQn is an automorphic graph, that is, FQn is a distance-transitive primitive graph which is not a complete or a line graph. [ABSTRACT FROM AUTHOR]