Automorphisms of augmented cubes

Abstract

A variation of the hypercube, the augmented cube AQ n of dimension n is defined as follows. It has 2 n vertices, each labelled by an n-bit binary string a 1 a 2···a n . Define AQ 1=K 2. For n≥2, AQ n is obtained by taking two copies and of AQ n−1, with vertex sets , , and joining 0 a 2 a 3···a n with 1 b 2 b 3···b n iff either (i) a 2 a 3···a n =b 2 b 3···b n , or (ii) . In this paper, we observe that AQ n is a Cayley graph and identify its automorphism group.