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    Heawood Graph

    Image

    Notation

    GH(1, 2)

    Basic properties

    vertex count | 14 edge count | 21 connected component count | 1

    Graph features

    arc-transitive | bicolorable | biconnected | bicubic | bipartite | biplanar | bridgeless | cage | Cayley graphs | class 1 | conformally rigid | connected | cubic | cyclic | determined by spectrum | distance-regular | distance-transitive | edge-transitive | flexible | fully reconstructible in C^1 | generalized polygon | geometric | Haar | Hamilton-decomposable | Hamiltonian | Hamilton-laceable | honeycomb toroidal | H-star connected | incidence | intrinsically linked | Knödel | LCF | local | Meyniel | Moore | multigraphic | nonempty | noneulerian | nonplanar | not uniquely embeddable | perfect | perfect matching | regular | simple | square-free | switchable | symmetric | toroidal | traceable | triangle-free | uniquely colorable | unit-distance | vertex-transitive | weakly perfect | weakly regular

    Complement graph

    14-vertex transitive graph 52

    Line graph

    generalized hexagon (2, 1)

    Graph degrees

    vertex degrees | 3 (14 vertices)

    Topological properties

    radius | 3 diameter | 3 girth | 6 vertex connectivity | 3 edge connectivity | 3

    Graph polynomials

    (x - 3) (x + 3) (x^2 - 2)^6

    x^13 y^8 + 21 x^13 y^7 + 210 x^13 y^6 + 1316 x^13 y^5 + 5712 x^13 y^4 + 17850 x^13 y^3 + 40096 x^13 y^2 + 61092 x^13 y + 50421 x^13 + 14 x^12 y^6 + ... + 115860 x^7 + 420 x^6 y + 54236 x^6 + 28 x^5 y + 20349 x^5 + 5985 x^4 + 1330 x^3 + 210 x^2 + 21 x + 1 (46 terms)

    x^13 + 8 x^12 + 36 x^11 + 120 x^10 + 330 x^9 + 28 x^8 y + 764 x^8 + 196 x^7 y + 1492 x^7 + 28 x^6 y^2 + 749 x^6 y + 2431 x^6 + 252 x^5 y^2 + ... + 679 x y^4 + 1806 x y^3 + 2730 x y^2 + 1883 x y + 317 x + y^8 + 13 y^7 + 77 y^6 + 273 y^5 + 637 y^4 + 973 y^3 + 861 y^2 + 317 y (45 terms)

    Coloring properties

    chromatic number | 2 edge chromatic number | 3

    Spectrum

    (-3)^1 (-sqrt(2))^6 sqrt(2)^6 3^1

    Associated matrices

    Graph indices

    Hosoya index | 3462 Kirchhoff index | 74.33 stability index | 7290 Wiener index | 189

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