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    30-vertex Transitive Graph 178

    Image

    Basic properties

    vertex count | 30 edge count | 75 connected component count | 1

    Graph features

    asymmetric | biconnected | bridgeless | class 1 | claw-free | connected | cyclic | fully reconstructible in C^1 | Hamilton-connected | Hamilton-decomposable | Hamiltonian | H-star connected | integral | LCF | line graphs | local | multigraphic | noncayley | nonempty | noneulerian | nongeometric | nonplanar | not determined by spectrum | not uniquely embeddable | pancyclic | perfect | perfect matching | permutation star | quintic | regular | rigid | simple | switchable | traceable | vertex-transitive | weakly perfect | weakly regular

    Complement graph

    (not a named graph)

    Line graph

    (not a named graph)

    Graph degrees

    vertex degrees | 5 (30 vertices)

    Topological properties

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

    Graph polynomials

    (x - 5) (x - 4)^5 x^9 (x + 1)^5 (x + 2)^10

    Coloring properties

    chromatic number | 5 edge chromatic number | 5

    Spectrum

    (-2)^10 (-1)^5 0^9 4^5 5^1

    Associated matrices

    Graph indices

    Hosoya index | 2.623 billion Kirchhoff index | 271.9 stability index | 990.8 million Wiener index | 1035