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    14-edge Transitive Graph 12

    Image

    Notation

    K_(3, 11)

    Basic properties

    vertex count | 14 edge count | 33 connected component count | 1

    Graph features

    apex | asymmetric | bicolorable | biconnected | bipartite | biplanar | bridgeless | class 1 | complete bipartite | complete k-partite | conformally rigid | connected | cyclic | distance-hereditary | edge-transitive | fully reconstructible in C^1 | graceful | linklessly embeddable | Meyniel | noncayley | nonempty | noneulerian | nongeometric | nonhamiltonian | nonplanar | no perfect matching | not uniquely embeddable | perfect | pretzel | rigid | simple | strongly perfect | switchable | triangle-free | uniquely colorable | untraceable | weakly perfect

    Complement graph

    (not a named graph)

    Line graph

    (not a named graph)

    Graph degrees

    vertex degrees | 3 (11 vertices) | 11 (3 vertices)

    Topological properties

    radius | 2 diameter | 2 girth | 4 vertex connectivity | 3 edge connectivity | 3

    Graph polynomials

    x^12 (x^2 - 33)

    x^13 y^20 + 33 x^13 y^19 + 528 x^13 y^18 + 11 x^12 y^18 + 5445 x^13 y^17 + 330 x^12 y^17 + 40590 x^13 y^16 + 4785 x^12 y^16 + 55 x^11 y^16 + ... + 10176111 x^8 + 3678048 x^7 + 1040688 x^6 + 232551 x^5 + 40755 x^4 + 5456 x^3 + 528 x^2 + 33 x + 1 (125 terms)

    y^20 + 13 y^19 + 11 x y^18 + 80 y^18 + 132 x y^17 + 312 y^17 + 55 x^2 y^16 + 748 x y^16 + 874 y^16 + 605 x^2 y^15 + 2684 x y^15 + ... + 210 x^11 + 1375 x^10 + 6105 x^9 + 19074 x^8 + 42966 x^7 + 70422 x^6 + 83490 x^5 + 69905 x^4 + 39259 x^3 + 13279 x^2 + 2045 x (124 terms)

    Coloring properties

    chromatic number | 2 edge chromatic number | 11

    Spectrum

    (-sqrt(33))^1 0^12 sqrt(33)^1

    Associated matrices

    Graph indices

    Hosoya index | 1354 Kirchhoff index | 51.21 stability index | 34 Wiener index | 149