n-dimensional Hamming cube

URI: https://gptkb.org/entity/n-dimensional_Hamming_cube
GPTKB entity
Statements (34)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
graph
gptkbp:alsoKnownAs gptkb:hypercube_graph
gptkbp:automorphismGroup hyperoctahedral group
gptkbp:chromaticNumber 2
gptkbp:cliqueNumber 2
gptkbp:degree n
gptkbp:diameter n
gptkbp:dimensions n
gptkbp:edge pair of vertices differing in exactly one bit
gptkbp:edgeCount n*2^{n-1}
gptkbp:embedding gptkb:n-dimensional_Euclidean_space
gptkbp:girth 4 (for n ≥ 2)
gptkbp:hasConnection true
https://www.w3.org/2000/01/rdf-schema#label n-dimensional Hamming cube
gptkbp:independenceNumber 2^{n-1}
gptkbp:isBipartite true
gptkbp:isCayleyGraph true
gptkbp:isDistanceRegular true
gptkbp:isEdgeTransitive true
gptkbp:isHamiltonian true
gptkbp:isPlanar true (for n ≤ 3), false (for n ≥ 4)
gptkbp:isRegular true
gptkbp:isVertexTransitive true
gptkbp:namedAfter gptkb:Richard_Hamming
gptkbp:relatedTo gptkb:algebra
gptkb:Gray_code
discrete mathematics
error-correcting codes
combinatorics
gptkbp:vertices 2^n
binary string of length n
gptkbp:bfsParent gptkb:(n-1)-dimensional_Hamming_cube
gptkbp:bfsLayer 7