JUCS - Journal of Universal Computer Science 6(1): 136-138, doi: 10.3217/jucs-006-01-0136
The Automorphism Group of a Hypercube
expand article infoFrank Harary‡
‡ Applied Computational Intelligence Laboratory, Department of Electrical and Computer Engineering, University of Missouri, Rolla, United States of America

Corresponding author: Frank Harary ( fnh@crl.nmsu.edu )

© Frank Harary.
This article is freely available under the J.UCS Open Content License.
Citation: Harary F (2000) The Automorphism Group of a Hypercube. JUCS - Journal of Universal Computer Science 6(1): 136-138. https://doi.org/10.3217/jucs-006-01-0136
Open Access
Abstract
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