|
gptkbp:instanceOf
|
gptkb:mathematical_concept
graph
|
|
gptkbp:alsoKnownAs
|
gptkb:n-cube_graph
|
|
gptkbp:automorphismGroup
|
hyperoctahedral group
|
|
gptkbp:bipartite
|
true
|
|
gptkbp:chromaticNumber
|
2
|
|
gptkbp:cliqueNumber
|
2
|
|
gptkbp:connects
|
true
|
|
gptkbp:definedIn
|
the graph formed from the vertices and edges of an n-dimensional hypercube
|
|
gptkbp:diameter
|
n
|
|
gptkbp:dimensions
|
n
|
|
gptkbp:edgeCount
|
n*2^{n-1}
|
|
gptkbp:edgeDefinition
|
edges connect vertices differing in exactly one coordinate
|
|
gptkbp:edgeTransitive
|
true
|
|
gptkbp:girth
|
4 for n>1
|
|
gptkbp:Hamiltonian
|
true
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
hypercube graph
|
|
gptkbp:independenceNumber
|
2^{n-1}
|
|
gptkbp:isCayleyGraph
|
true
|
|
gptkbp:isDistanceRegular
|
true
|
|
gptkbp:isEdgeColorable
|
true
|
|
gptkbp:isEulerian
|
true if n is even
|
|
gptkbp:isHamiltonianConnected
|
true
|
|
gptkbp:isMedianGraph
|
true
|
|
gptkbp:isPartialCube
|
true
|
|
gptkbp:isSubgraphOf
|
gptkb:complete_graph_K_{2^n}
|
|
gptkbp:isSymmetricGraph
|
true
|
|
gptkbp:isVertexColorable
|
true
|
|
gptkbp:maximumDegree
|
n
|
|
gptkbp:minimumDegree
|
n
|
|
gptkbp:OEIS
|
gptkb:A000079_(number_of_vertices)
A001787 (number of edges)
|
|
gptkbp:planar
|
false for n>3
|
|
gptkbp:regularity
|
n-regular
|
|
gptkbp:relatedTo
|
gptkb:Hamming_distance
gptkb:Boolean_cube
gptkb:Gray_code
gptkb:cube-connected_cycles
gptkb:de_Bruijn_graph
|
|
gptkbp:selfComplementary
|
true
|
|
gptkbp:studiedBy
|
gptkb:Hugo_Steinhaus
|
|
gptkbp:usedIn
|
coding theory
combinatorics
network topology
parallel computing
|
|
gptkbp:vertexLabeling
|
binary n-tuples
|
|
gptkbp:vertexTransitive
|
true
|
|
gptkbp:vertices
|
2^n
|
|
gptkbp:WolframMathWorldID
|
HypercubeGraph.html
|
|
gptkbp:bfsParent
|
gptkb:Hamming_graph
gptkb:Weyl_group
|
|
gptkbp:bfsLayer
|
5
|