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    Hoffman-Singleton Graph

    Image

    Image

    Basic properties

    vertex count | 50
edge count | 175
connected component count | 1

    Graph features

    arc-transitive | biconnected | bridgeless | cage | class 1 | connected | cyclic | determined by spectrum | distance-regular | distance-transitive | edge-transitive | Hamilton-connected | Hamilton-decomposable | Hamiltonian | H-star connected | imperfect | integral | LCF | local | Moore | nonempty | noneulerian | nonplanar | perfect matching | regular | septic | simple | square-free | strongly regular | symmetric | traceable | triangle-free | vertex-transitive

    Complement graph

    Hoffman-Singleton graph complement

    Graph degrees

    vertex degrees | 7 (50 vertices)

    Topological properties

    radius | 2
diameter | 2
girth | 5
vertex connectivity | 7
edge connectivity | 7

    Graph polynomials

    (x - 7) (x - 2)^28 (x + 3)^21

    Coloring properties

    chromatic number | 4
edge chromatic number | 7

    Spectrum

    (-3)^21 2^28 7^1

    Associated matrices

    Associated matrices Adjacency matrix

    Associated matrices Incidence matrix

    Graph indices

    Kirchhoff index | 385
stability index | 2.651×10^21
Wiener index | 2275

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