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    Conway-Smith Graph

    Image

    Image

    Basic properties

    vertex count | 63
edge count | 315
connected component count | 1

    Graph features

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

    Complement graph

    (not a named graph)

    Line graph

    (not a named graph)

    Graph degrees

    vertex degrees | 10 (63 vertices)

    Topological properties

    radius | 4
diameter | 4
girth | 3
vertex connectivity | 10
edge connectivity | 10

    Graph polynomials

    (x - 10) (x - 5)^12 (x - 1)^14 (x + 2)^30 (x + 4)^6

    Coloring properties

    chromatic number | 5
edge chromatic number | 11

    Spectrum

    (-4)^6 (-2)^30 1^14 5^12 10^1

    Associated matrices

    Associated matrices Adjacency matrix

    Graph indices

    Kirchhoff index | 433.7
stability index | 5.133×10^25
Wiener index | 4347

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