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    Gray Graph

    Image

    Image

    Basic properties

    vertex count | 54 edge count | 81 connected component count | 1

    Graph features

    asymmetric | bicolorable | biconnected | bicubic | bipartite | bridgeless | class 1 | connected | cubic | cyclic | edge-transitive | Hamilton-decomposable | Hamiltonian | Hamilton-laceable | H-star connected | incidence | LCF | local | noncayley | nonempty | noneulerian | nonplanar | perfect | perfect matching | regular | semisymmetric | simple | square-free | traceable | triangle-free | weakly perfect | weakly regular

    Complement graph

    (not a named graph)

    Line graph

    (not a named graph)

    Graph degrees

    vertex degrees | 3 (54 vertices)

    Topological properties

    radius | 6 diameter | 6 girth | 8 vertex connectivity | 3 edge connectivity | 3

    Graph polynomials

    (x - 3) x^16 (x + 3) (x^2 - 6)^6 (x^2 - 3)^12

    Coloring properties

    chromatic number | 2 edge chromatic number | 3

    Spectrum

    (-3)^1 (-sqrt(6))^6 (-sqrt(3))^12 0^16 sqrt(3)^12 sqrt(6)^6 3^1

    Associated matrices

    Associated matrices Adjacency matrix

    Associated matrices Incidence matrix

    Graph indices

    Hosoya index | 43.61 trillion Kirchhoff index | 1593 stability index | 19.74 trillion Wiener index | 5481

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