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    (9, 2)-Hamming Graph

    Image

    Notation

    Q_9

    Basic properties

    vertex count | 512 edge count | 2304 connected component count | 1

    Graph features

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

    Graph degrees

    vertex degrees | 9 (512 vertices)

    Topological properties

    radius | 9 diameter | 9 girth | 4 vertex connectivity | 9 edge connectivity | 9

    Graph polynomials

    (x - 9) (x - 7)^9 (x - 5)^36 (x - 3)^84 (x - 1)^126 (x + 1)^126 (x + 3)^84 (x + 5)^36 (x + 7)^9 (x + 9)

    Coloring properties

    chromatic number | 2 edge chromatic number | 9

    Spectrum

    (-9)^1 (-7)^9 (-5)^36 (-3)^84 (-1)^126 1^126 3^84 5^36 7^9 9^1

    Associated matrices

    Graph indices

    Kirchhoff index | 33812 stability index | 1.184×10^190 Wiener index | 589824

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