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    Hexeract Graph

    Image

    Notation

    Q_6

    Basic properties

    vertex count | 64 edge count | 192 connected component count | 1

    Graph features

    antipodal | arc-transitive | bicolorable | biconnected | bipartite | biplanar | bridgeless | Cayley graphs | class 1 | connected | cyclic | distance-regular | distance-transitive | edge-transitive | Eulerian | graceful | grid | Hamilton-decomposable | Hamiltonian | Hamilton-laceable | Hamming | H-star connected | hypercube | incidence | integral | LCF | local | median | nonempty | nonplanar | perfect | perfect matching | regular | sextic | simple | symmetric | traceable | triangle-free | uniquely colorable | unit-distance | vertex-transitive | weakly perfect | weakly regular | zero-two

    Complement graph

    (not a named graph)

    Line graph

    (not a named graph)

    Graph degrees

    vertex degrees | 6 (64 vertices)

    Topological properties

    radius | 6 diameter | 6 girth | 4 vertex connectivity | 6 edge connectivity | 6

    Graph polynomials

    (x - 6) (x - 4)^6 (x - 2)^15 x^20 (x + 2)^15 (x + 4)^6 (x + 6)

    Coloring properties

    chromatic number | 2 edge chromatic number | 6

    Spectrum

    (-6)^1 (-4)^6 (-2)^15 0^20 2^15 4^6 6^1

    Associated matrices

    Graph indices

    Hosoya index | 7.175×10^21 Kirchhoff index | 809.1 stability index | 2.725×10^19 Wiener index | 6144

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