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    Benson Graph

    Image

    Notation

    GD(1, 2)

    Basic properties

    vertex count | 126 edge count | 189 connected component count | 1

    Graph features

    asymmetric | bicolorable | biconnected | bicubic | bipartite | bridgeless | cage | class 1 | connected | cubic | cyclic | determined by spectrum | distance-regular | edge-transitive | generalized polygon | Hamilton-decomposable | Hamiltonian | Hamilton-laceable | H-star connected | LCF | local | Moore | noncayley | nonempty | noneulerian | nonplanar | perfect | perfect matching | regular | semisymmetric | simple | square-free | traceable | triangle-free | uniquely colorable | unit-distance | weakly perfect | weakly regular

    Line graph

    generalized dodecagon (2, 1)

    Graph degrees

    vertex degrees | 3 (126 vertices)

    Topological properties

    radius | 6 diameter | 6 girth | 12 vertex connectivity | 3 edge connectivity | 3

    Graph polynomials

    (x - 3) x^28 (x + 3) (x^2 - 6)^21 (x^2 - 2)^27

    Coloring properties

    chromatic number | 2 edge chromatic number | 3

    Spectrum

    (-3)^1 (-2.44949)^21 (-1.41421)^27 0^28 1.41421^27 2.44949^21 3^1

    Associated matrices

    Graph indices

    Kirchhoff index | 9405 stability index | 4.259×10^31 Wiener index | 36477

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