DistanceRegular.org
3-cube $Q_3 \cong H(3,2) \cong K_{4,4}-I$
Number of vertices:
$8$
Diameter:
$3$
Intersection array:
$\{3,2,1; 1,2,3\}$
Spectrum:
$3^1 1^3 (-1)^3 (-3)^1$
Automorphism group:
$\mathbb{Z}_2\text{Wr}S_3$
Distance-transitive:
Yes
Bipartite
,
Antipodal
Downloads
Adjacency matrix
Adjacency matrix in GAP format
Adjacency matrix in CSV format
Graph in GRAPE format
Links
Andries Brouwer: Hamming graph $H(d,q)$
Wikipedia: Hamming graph $H(d,q)$
Wolfram: Hamming graph $H(d,q)$
Wikipedia: Hypercube graph $H(d,2)$
Wolfram: Hypercube graph $H(d,2)$
Wikipedia: Crown graph $K_{n,n}-I$
Wolfram: Crown graph $K_{n,n}-I$
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Graphs with up to 50 vertices
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Graphs with diameter 3
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Graphs with valency 3
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Crown Graphs
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Hamming Graphs
Last updated: 4 February 2017