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    Conway-Smith Graph

    Image

    Basic properties

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

    Graph features

    arc-transitive | biconnected | bridgeless | class 2 | conformally rigid | connected | cyclic | distance-regular | distance-transitive | edge-transitive | Eulerian | fully reconstructible in C^1 | Hamilton-connected | Hamilton-decomposable | Hamiltonian | H-star connected | imperfect | integral | intrinsically linked | LCF | local | locally Petersen | multigraphic | nonempty | nongeometric | nonplanar | no perfect matching | not uniquely embeddable | pancyclic | regular | rigid | simple | switchable | 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

    Graph indices

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