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    Brouwer-Haemers Graph

    Image

    Image

    Alternate name

    local (3, 9)-generalized quadrangle

    Basic properties

    vertex count | 81 edge count | 810 connected component count | 1

    Graph features

    arc-transitive | biconnected | bridgeless | class 2 | connected | cyclic | determined by spectrum | distance-regular | distance-transitive | edge-transitive | Eulerian | Hamilton-connected | Hamilton-decomposable | Hamiltonian | H-star connected | imperfect | integral | LCF | local | nonempty | nonplanar | no perfect matching | pancyclic | regular | simple | strongly regular | symmetric | traceable | ungraceful | vertex-transitive

    Complement graph

    (not a named graph)

    Graph degrees

    vertex degrees | 20 (81 vertices)

    Topological properties

    radius | 2 diameter | 2 girth | 3 vertex connectivity | 20 edge connectivity | 20

    Graph polynomials

    -((x - 20) (x - 2)^60 (x + 7)^20)

    Coloring properties

    chromatic number | 7 edge chromatic number | 21

    Spectrum

    (-7)^20 2^60 20^1

    Associated matrices

    Associated matrices Adjacency matrix

    Graph indices

    Kirchhoff index | 330 stability index | 1.628×10^45 Wiener index | 5670

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