Automorphisms of augmented cubes

A variation of the hypercube, the augmented cube AQn of dimension n is defined as follows. It has 2n vertices, each labelled by an n-bit binary string a1a2 ? ? ? an. DefineAQ1 = K2. For n =≥ 2,AQn is obtained by taking two copies AQ0n-1 and AQ1n-1 of AQn-1, with vertex sets V (AQ0n-1) = {0a2a3 ? ? ? an : a i = 0 or 1}, V (AQ1n-1) = {1b 2b3 ? ? ? bn : bi = 0 or 1}, and joining 0a2a3 ? ? ? an with 1b2b3 ? ? ? bn iff either (i) a2a3 ? ? ? an = b2b3 ? ? ? bn, or (ii) a2a 3 ? ? ? an = b2b3 ? ? ? b n. In this paper, we observe that AQn is a Cayley graph and identify its automorphism group.