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    Frucht Graph

    Image

    Basic properties

    vertex count | 12 edge count | 18 connected component count | 1

    Graph features

    apex | asymmetric | biconnected | bridgeless | class 1 | connected | cubic | cyclic | Halin | Hamilton-connected | Hamilton-decomposable | Hamiltonian | H-star connected | identity | imperfect | LCF | noncayley | nonempty | noneulerian | pancyclic | perfect matching | planar | polyhedral | projective planar | regular | simple | traceable | unit-distance | weakly perfect | weakly regular

    Complement graph

    (not a named graph)

    Dual graph

    8-triangulated graph 2

    Line graph

    (not a named graph)

    Graph degrees

    vertex degrees | 3 (12 vertices)

    Topological properties

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

    Graph polynomials

    (x - 3) (x - 2) x (x + 1) (x + 2) (x^3 + x^2 - 2 x - 1) (x^4 + x^3 - 6 x^2 - 5 x + 4)

    x^11 y^7 + 18 x^11 y^6 + 153 x^11 y^5 + 800 x^11 y^4 + 2788 x^11 y^3 + 6479 x^11 y^2 + 9264 x^11 y + 6235 x^11 + 16 x^10 y^5 + 272 x^10 y^4 + 2042 x^10 y^3 + ... + 8236 x^5 + 4 x^4 y^2 + 332 x^4 y + 3014 x^4 + 46 x^3 y + 813 x^3 + 3 x^2 y + 153 x^2 + 18 x + 1 (44 terms)

    x^11 + 7 x^10 + 3 x^9 y + 25 x^9 + 19 x^8 y + 62 x^8 + 4 x^7 y^2 + 64 x^7 y + 120 x^7 + 25 x^6 y^2 + 152 x^6 y + 191 x^6 + 4 x^5 y^3 + ... + 16 x y^5 + 113 x y^4 + 304 x y^3 + 379 x y^2 + 206 x y + 32 x + y^7 + 11 y^6 + 50 y^5 + 120 y^4 + 160 y^3 + 112 y^2 + 32 y (43 terms)

    Coloring properties

    chromatic number | 3 edge chromatic number | 3

    Spectrum

    (root of 4 - 5 x - 6 x^2 + x^3 + x^4 near x = -2.33866)^1 (-2)^1 (root of -1 - 2 x + x^2 + x^3 near x = -1.80194)^1 (root of 4 - 5 x - 6 x^2 + x^3 + x^4 near x = -1.45106)^1 (-1)^1 (root of -1 - 2 x + x^2 + x^3 near x = -0.445042)^1 0^1 (root of 4 - 5 x - 6 x^2 + x^3 + x^4 near x = 0.51912)^1 (root of -1 - 2 x + x^2 + x^3 near x = 1.24698)^1 2^1 (root of 4 - 5 x - 6 x^2 + x^3 + x^4 near x = 2.2706)^1 3^1

    Associated matrices

    Graph indices

    Hosoya index | 1026 Kirchhoff index | 60.46 stability index | 820 Wiener index | 139

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