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.