n-dimensional Hamming cube

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:mathematical_concept gptkb: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
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:combinatorics gptkb:algebra gptkb:Gray_code discrete mathematics error-correcting codes
gptkbp:vertices	2^n binary string of length n
gptkbp:bfsParent	gptkb:(n-1)-dimensional_Hamming_cube
gptkbp:bfsLayer	7
https://www.w3.org/2000/01/rdf-schema#label	n-dimensional Hamming cube