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    Sylvester Graph

    Image

    Image

    Basic properties

    vertex count | 36
edge count | 90
connected component count | 1

    Graph features

    arc-transitive | biconnected | bridgeless | 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 | nonempty | noneulerian | nonplanar | perfect matching | quintic | regular | simple | square-free | symmetric | traceable | triangle-free | vertex-transitive | weakly regular

    Complement graph

    (not a named graph)

    Line graph

    (not a named graph)

    Graph degrees

    vertex degrees | 5 (36 vertices)

    Topological properties

    radius | 3
diameter | 3
girth | 5
vertex connectivity | 5
edge connectivity | 5

    Graph polynomials

    (x - 5) (x - 2)^16 (x + 1)^10 (x + 3)^9

    Coloring properties

    chromatic number | 4
edge chromatic number | 5

    Spectrum

    (-3)^9 (-1)^10 2^16 5^1

    Associated matrices

    Associated matrices Adjacency matrix

    Associated matrices Incidence matrix

    Graph indices

    Hosoya index | 237.8 billion
Kirchhoff index | 292.5
stability index | 2.028 trillion
Wiener index | 1350

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