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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.
Acknowledgements
We would like to thank the referees for several suggestions, which enabled us to improve the presentation of the paper; and S. Lavanya and R. Indhumathi for a lively discussion on the revisions.