The Automorphism Group of a Hypercube
Frank Harary (Applied Computational Intelligence Laboratory, Department of Electrical and Computer Engineering, University of Missouri, USA)
We present explicitly in this expository note the automorphism group of the hypercube Qd of dimension d as a permutation group acting on its 2d nodes. This group (Qd) acts on the node set Vd of Qd and thus has degree 2d. It is expressed as the binary operation called exponentiation which combines the two symmetric groups S2 (of degree and order 2) and Sd (of degree d and order d!). Specifically,
(Qd) = [S2]Sd.
has order 2dd!.
1 C.S.Calude and G.Stefanescu (eds.). Automata, Logic, and Computability. Special issue dedicated to Professor Sergiu Rudeanu Festschrift.
Keywords: automorphism group, hypercube, permutation graph