The Automorphism Group of a Hypercube

Frank Harary (Applied Computational Intelligence Laboratory, Department of Electrical and Computer Engineering, University of Missouri, USA)

Abstract:

We present explicitly in this expository note the automorphism group of the hypercube Q_d of dimension d as a permutation group acting on its 2^d nodes. This group (Q_d) acts on the node set V_d of Q_d and thus has degree 2^d. It is expressed as the binary operation called exponentiation which combines the two symmetric groups S₂ (of degree and order 2) and S_d (of degree d and order d!). Specifically,

has order 2^dd!.

Keywords: automorphism group, hypercube, permutation graph

Categories: F.4.1