n-dimensional hypercube graph

URI: https://gptkb.org/entity/n-dimensional_hypercube_graph
GPTKB entity
Statements (51)
Predicate Object
gptkbp:instanceOf gptkb:Weyl_group
gptkb:mathematical_concept
graph
gptkbp:alsoKnownAs gptkb:hypercube_graph
Q_n
gptkbp:automorphismGroup hyperoctahedral group
gptkbp:chromaticNumber 2
n
gptkbp:diameter n
gptkbp:edge n*2^{n-1}
gptkbp:embeddingDimension n
gptkbp:girth 4
gptkbp:hasApplication coding theory
combinatorics
network topology
parallel computing
gptkbp:hasConnection true
https://www.w3.org/2000/01/rdf-schema#label n-dimensional hypercube graph
gptkbp:isBipartite true
gptkbp:isCartesianProductOf n copies of K_2
gptkbp:isCayleyGraphOf (Z_2)^n
gptkbp:isDistanceRegular true
gptkbp:isDistanceTransitive true
gptkbp:isEdgeColorable true
gptkbp:isEdgeSet pairs of binary strings differing in one bit
gptkbp:isEdgeSymmetric true
gptkbp:isEdgeTransitive true
gptkbp:isEulerian true if n is even
false if n is odd
gptkbp:isHamiltonian true
gptkbp:isInducedSubgraphOf (n+1)-dimensional hypercube graph
gptkbp:isMedianGraph true
gptkbp:isPartialCube true
gptkbp:isPerfect true
gptkbp:isPlanar false
gptkbp:isRegular true
gptkbp:isSelfComplementary true
gptkbp:isUnitDistanceGraph true
gptkbp:isVertexColorable true
gptkbp:isVertexSet all binary strings of length n
gptkbp:isVertexSymmetric true
gptkbp:isVertexTransitive true
gptkbp:maximumDegree n
gptkbp:minimumDegree n
gptkbp:minimumEdgeCut n*2^{n-1}
gptkbp:minimumVertexCut n
gptkbp:symmetry true
gptkbp:vertexDegree n
gptkbp:vertices 2^n
gptkbp:bfsParent gptkb:Boolean_cube
gptkbp:bfsLayer 7